Alright. Here is probably the best list for character supports. I am ranking these as best for the supportee, not on team comp or what the supporter will get in return; though I will note any major issues.
Ike: Oscar, Soren, Titania, Lethe, Reyson, Ranulf, Elincia. Lethe trumps Reyson due to join time and that the difference will be 1 ATT at B-level which isn't going to be a big thing at all for Ike.
Titania: Rhys, Mist, Ike (B), Boyd, Ike (A). An A Ike takes 26 chapters to complete and only gives Titania a bit more AVO (2.5) than if she just took the B. Even then the Rhys support offers Titania +1 attack which, when compared to the 5 avoid... isn't much. Holding out for Mist is a better choice.
Oscar: Ike, Kieran, Tanith >= Janaff. Janaff, while faster on the support, only finishes one chapter behind and the extra 5 AVO is worth-while on an avoid-heavy unit with solid defenses already.
Boyd: Mist, Brom (B), Ulki, Brom (A), Titania. A Titania support just is outclassed by the +3 ATT the other supports offer.
Rhys: Mia > All the rest. The only support that, arguably, helps Rhys out is Mia's since it can give his attacks a bit more oomph when he promotes. If this should be a common thing or rarity is up to the player, but the other supports simply don't address his real problem, SPD. He's not likely to dodge and his DEF is low enough for the extra point to likely not matter.
Shinon: Janaff >=< Rolf, Gatrie. Who wins in Rolf vs. Janaff will depend on how willing you are to keep the hawk close to a sniper. If you are Janaff and the DEF boost he'll give is better. If not Rolf and his speed and AVO boost trump.
Gatrie: Ilyana, Astrid = Marcia, Shinon. While the extra DEF is nice, as a general, Gatrie's problem lies in his AS. He's not likely to double rendering the attack moot, doesn't have defensive problems, and so-forth. Ilyana will give him an early +3 DEF... and the other two are pretty much pointless with Shinon and his lateness coming in last.
Soren: Ike > Stefan. Well... yea.
Mia: Rhys > Ilyana > Largo. Largo, while technically better from a statistical standpoint, simply joins too late and the ATT boost from Rhys and +1 ATT/DEF from Ilyana that won't wait till super-late simply trumps the avoid given by Largo.
Ilyana: Mordi > Gatrie > Zihark > Mia > Lucia. Lucia just joins too late. Don't be fooled though. Pretty much all of Ilyana's supports are middling and which ones you pick should depend more on how you want to build her and who else you're using than a simple priority list. None suck or really stand out beyond a potential Mordi/Gatrie double.
Marcia: Keiran >= Rolf >= Tanith >= Gatire. All of Marcia's supports are meh and don't give her much. Kieran wins because he's easier to keep close, Rolf gives her AVO and is fast on the support, Tanith gives MORE AVO and will be close but joins late, and Gatrie joins early but doesn't give her much. Better for her just to snap up leftovers.
Mist: Mordi > Jill > Titania = Boyd > Rolf. Rolf just doesn't mesh with water while Mordi gives +3 ATT/DEF at A and Jill gives some nice DEF and avoid. Titania vs. Boyd depends on if you want to focus on attack or defense.
Rolf: Mist > Rhys > Marcia > Shinon > Tauro
Lethe: Jill > Ike > Muarim > Ranulf. All give AVO, which is nice, with Ike giving more AVO and Jill/Muarim giving DEF. Ranulf just joins too late.
Mordi: Mist > Ilyana > Ulki > Stefan > Ranulf. Mist has a perfect synergy and Ilyana gives good DEF. Ulki gives some great bonuses but might be too late. Stefan just gives hit which he doesn't need and Ranulf doesn't mesh and joins too late.
Volke: Bastion.
Kieran: Oscar > Marcia > Rhys. Marcia might take longer but she'll be easier to keep close.
Brom: Boyd, Neph=Zihark. Brom's not dodging much, so the ATT boost from Boyd wins out.
Nephenee: Brom > Devdan > Calill. Calill just joins too late.
Zihark: Muarim > Brom > Ilyana.
Sothe: Astrid > Tormod. Sothe should not be deployed since he can't promote. Astrid at least meshes with him for double avoid though.
Jill: Mist > Lethe > Haar. Haar joins too late.
Astrid: Malalov > Gatrie > Sothe. Even though Sothe is better Sothe's low stats and limited use is pretty much the only spot on this list where a unit not being deployed will matter. At least Gatrie will be on the map.
Makalov: Astrid > Haar > Bastion
Stefan: Soren > Mordi
Tormod: Devdan = Reyson > Calill > Sothe. Waiting for Calill gives an ATT boost.
Muarim: Zihark > Lethe > Largo
Devdan: Tormod > Nephenee > Largo
Reyson: Ike > Tanith > Tormod. Reyson won't ever attack.
Ulki: Mordi > Boyd > Rhys
Janaff: Oscar > Shinon > Lucia
Tanith: Oscar > Marcia > Reyson
Calill: Tormod > Nephenee > Geoffry
Tauro: Rolf = Largo.
Ranulf: Ike > Mordi > Lethe
Haar: Jill > Makalov
Lucia: Janaff > Bastion > Ilyana
Bastion: Lucia > Makalov > Volke
Geoffry: Calill > Elincia
Largo: Muarim > Tauro > Mia = Devdan
Elincia: Ike >= Geoffry. Aside from RNG abuse Elincia is unlikely to be strong enough for the ATT to matter. Neither should come into play more than once though.
