Agree that Ghave and Sharuum are top notch for infinite combos.
However.
Q: Best way to assemble combos?
A: Tutors.
Here BUG reigns supreme. Black tutors anything, Blue tutors sorcery, instant, and artifact, Green tutors creatures.
Q: What infinite combos are the best to assemble?
A: Infinite Turns & Infinite Mana
Here BUG reigns supreme again. B/U hosts infi-mana the best, and U/G hosts infi-turns.
BUG clearly is the best infinite combo color.
As for "which general has the most" seems like the wrong question to be asking. How many do you need?
That's not even the right question to answer. The question to answer is "which is the best combo?" What makes a combo the best (in theory) is debatable. I think it's a combination of several factors: Reliability, Durability, number of options in the event of failure, number of options before assembly, and speed of assembly, to name a few. Here, I think green/white/(x) reins supreme, because of the strength of the individual pieces usually allowing you to keep up with others before you assemble it, as well as allowing you to continue playing with a chance at victory in the event of failure. Green is no slouch at tutoring either, in fact it rivals black in that department, if all you're tutoring for are creatures. Though it also helps that green white tends to fly under the radar in my experience.
As a variant on the Power Artifact/Basalt Monolith combo, there's also Rings of Brightearth. This also combos with a land whose name has escaped me. Palinchron is a one card combo engine, and anything that clones it or whatever for less than seven mana will go infinite. Phyrexian Metamorph, Phantasmal Image, Clone, etc. Also, Mind Over Matter and Temple Bell, Sanguine Bond and Exquisite Blood.
Anything running green gets Aluren which goes crazy with any constant repeatable bounce effect. Someone has already mentioned Cloudstone Curio (honorable mention: Equilibrium) which works with Aluren to trigger an infinite number or ETB effects, or put an infinite number of +1/+1 counters on Animar.
You can also have Teysa, Orzhov Scion + Darkest Hour + Any Creature + Viscera Seer to scry to a win con and Teysa, Orzhov Scion + Darkest Hour + Any Creature + Sadistic Hypnotist to universal discard. Both of those can win with Blood Artist in play as well. The Infinite Mana Loops can combo with Mentor of the Meek or Skullclamp to draw your deck to find a win condition. You can loop Duplicant with any Reveillark Loop that you can't win with to remove everyone's creatures. I'm sure there's more loops like with Altar of Dementia replacing Blasting Station or Phyrexian Altar, but those are what I believe to be all the ways I can combo in my Teysa deck. I had Nezumi Graverobber in the deck for awhile, I might add it back in. Still experimenting with the "hate card" slots, but with infinite mana you can loop things from the yard which is pretty cool. Don't freak out if one of these combos doesn't work the way I think it does, I'm quite sure every one is possible, the only one I'm not 100% correct on despite getting it checked by a friend that's a rules guru is #'s 10-12. The whole Sun Titan and double reanimate enchantments, the triggers are confusing.
I went through and found the number for each color combo from colorless to the 4 colors (excluding WUBRG for obvious reasons). Obviously the three and four color combos have more than the one or two but regardless the order from most to least is as follows (this is from info gathered from the commander spellbook website to find infinites which I highly recommend)
Ink-Treader(RGWU):18583
Witch-Maw(GWUB):18222
Glint-Eye(UBRG):18145
Yore-Tiller(WUBR):16734
Dune-Brood(BRGW):14132
Bant:10768
Temur:10748
Sulti:10582
Grixis:10054
Jeskai:9802
Esper:9273
Naya7943
Abzan:7925
Jund:7694
Mardu:7217
Simic:6090
Izzet:5540
Dimir:5113
Azorious:5002
Golgari:4041
Selesnya:3951
Rakdos:3905
Gruul:3885
Boros:3703
Orzhov:3581
Blue:2603
Green:1817
Black:1700
Red:1696
White:1459
Colorless:500
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However.
Q: Best way to assemble combos?
A: Tutors.
Here BUG reigns supreme. Black tutors anything, Blue tutors sorcery, instant, and artifact, Green tutors creatures.
Q: What infinite combos are the best to assemble?
A: Infinite Turns & Infinite Mana
Here BUG reigns supreme again. B/U hosts infi-mana the best, and U/G hosts infi-turns.
BUG clearly is the best infinite combo color.
As for "which general has the most" seems like the wrong question to be asking. How many do you need?
Modern
RBig RedR
GMean GreenG
WWW AlliesW
BGScavengeBG
WUVenser SilenceWU
EDH
RWAurelia 1 vs 1RW
GWURoonGWU
GWSaffiGW
That's not even the right question to answer. The question to answer is "which is the best combo?" What makes a combo the best (in theory) is debatable. I think it's a combination of several factors: Reliability, Durability, number of options in the event of failure, number of options before assembly, and speed of assembly, to name a few. Here, I think green/white/(x) reins supreme, because of the strength of the individual pieces usually allowing you to keep up with others before you assemble it, as well as allowing you to continue playing with a chance at victory in the event of failure. Green is no slouch at tutoring either, in fact it rivals black in that department, if all you're tutoring for are creatures. Though it also helps that green white tends to fly under the radar in my experience.
Animar has sooo many combos, it's rediculous, almost every creature does something to help with comboing into free Eldrazi and bounce triggers.
Decks:
WUG Jenara, Asura of War
WR Kalemne, Disciple of Iroas
WU Lavinia of the Tenth
UR Mizzix of the Izmagnus
As a variant on the Power Artifact/Basalt Monolith combo, there's also Rings of Brightearth. This also combos with a land whose name has escaped me. Palinchron is a one card combo engine, and anything that clones it or whatever for less than seven mana will go infinite. Phyrexian Metamorph, Phantasmal Image, Clone, etc. Also, Mind Over Matter and Temple Bell, Sanguine Bond and Exquisite Blood.
Anything running green gets Aluren which goes crazy with any constant repeatable bounce effect. Someone has already mentioned Cloudstone Curio (honorable mention: Equilibrium) which works with Aluren to trigger an infinite number or ETB effects, or put an infinite number of +1/+1 counters on Animar.
Oh Rider, my heart will go on...
1. Teysa, Orzhov Scion + Blasting Station + Darkest Hour + Any Creature
2. Teysa, Orzhov Scion + Phyrexian Altar + Nether Traitor + Bitter Ordeal
3. Teysa, Orzhov Scion + Phyrexian Altar + Nether Traitor + Blood Artist
4. Teysa, Orzhov Scion + Phyrexian Altar + Nether Traitor + Blasting Station
5. Teysa, Orzhov Scion + Phyrexian Altar + Nether Traitor + Mortarpod (Stoneforge Mystic/Steelshaper's Gift)
6. Phyrexian Altar + Reveillark + Karmic Guide + Blood Artist
7. Phyrexian Altar + Reveillark + Karmic Guide + Bitter Ordeal
8. Blasting Station + Reveillark + Karmic Guide
9. Blasting Station + Sun Titan + Necromancy/Animate Dead + Karmic Guide
10. Phyrexian Altar + Sun Titan + Animate Dead + Necromancy + Any Creature +Bitter Ordeal
11. Phyrexian Altar + Sun Titan + Animate Dead + Necromancy + Any Creature + Blood Artist
12. Blasting Station + Sun Titan + Animate Dead + Necromancy + Any Creature
13. Teysa, Orzhov Scion + Darkest Hour + Phyrexian Altar + Any Creature + Blood Artist
14. Teysa, Orzhov Scion + Darkest Hour + Phyrexian Altar + Any Creature + Bitter Ordeal
15. Teysa, Orzhov Scion + Darkest Hour + Phyrexian Altar + Mortarpod
16. Sadistic Hypnotist + Reveillark + Karmic Guide + Blood Artist
17. Sadistic Hypnotist + Reveillark + Karmic Guide + Bitter Ordeal
18. Viscera Seer + Reveillark + Karmic Guide + Blood Artist
19. Viscera Seer + Reveillark + Karmic Guide + Bitter Ordeal
20. Teysa, Orzhov Scion + Reveillark + Karmic Guide + Blood Artist
21. Teysa, Orhov Scion + Reveillark + Karmic Guide + Any Creature + Bitter Ordeal
You can also have Teysa, Orzhov Scion + Darkest Hour + Any Creature + Viscera Seer to scry to a win con and Teysa, Orzhov Scion + Darkest Hour + Any Creature + Sadistic Hypnotist to universal discard. Both of those can win with Blood Artist in play as well. The Infinite Mana Loops can combo with Mentor of the Meek or Skullclamp to draw your deck to find a win condition. You can loop Duplicant with any Reveillark Loop that you can't win with to remove everyone's creatures. I'm sure there's more loops like with Altar of Dementia replacing Blasting Station or Phyrexian Altar, but those are what I believe to be all the ways I can combo in my Teysa deck. I had Nezumi Graverobber in the deck for awhile, I might add it back in. Still experimenting with the "hate card" slots, but with infinite mana you can loop things from the yard which is pretty cool. Don't freak out if one of these combos doesn't work the way I think it does, I'm quite sure every one is possible, the only one I'm not 100% correct on despite getting it checked by a friend that's a rules guru is #'s 10-12. The whole Sun Titan and double reanimate enchantments, the triggers are confusing.
EDH:
Teysa Combo
If you're talking about infini-combos with the general as part of it, Niv-Mizzet and Sharuum are the best, Animar a close second
Ink-Treader(RGWU):18583
Witch-Maw(GWUB):18222
Glint-Eye(UBRG):18145
Yore-Tiller(WUBR):16734
Dune-Brood(BRGW):14132
Bant:10768
Temur:10748
Sulti:10582
Grixis:10054
Jeskai:9802
Esper:9273
Naya7943
Abzan:7925
Jund:7694
Mardu:7217
Simic:6090
Izzet:5540
Dimir:5113
Azorious:5002
Golgari:4041
Selesnya:3951
Rakdos:3905
Gruul:3885
Boros:3703
Orzhov:3581
Blue:2603
Green:1817
Black:1700
Red:1696
White:1459
Colorless:500