What projects should I start if I want to make teams for GHB? What should the order be?

Horse Emblem is by far the easiest to build. The key skills like Hone and Fortify Cavalry are available at 3-4 stars and you already have some of the best horses: Reinhardt, Cecilia, and Xander. This would be a good place to start.

Going from neutral stats (don't know their IVs) I would use...

Infantry Emblem
--
Chrom (Falchion Refinement) or Marisa
Nino
Sharena (to buff Nino)
Nowi

Armor
--
Eliwood
Black Knight
Sheena
Zephiel

Cavalry
--
Lyn
Reinhardt
Cecilia
Xander

Flier
--
Camilla
Cordelia
Myrrh
Cherche(For huge damage) or Beruka (huge defense)

Of course, what really matters is what builds each unit has.

Right now, you can make a good infantry team, good armor team, decent flier team and decent cavalry team. Personally, id start with infantry and armor. Try to get a better red infantry unit that isnt support, but the ones you have now are A-ok.

Units are nice to have, however not having SI when you need it for certain maps (like my stockpile of Pallas I just depleted for WOM to do the flier quest on GHB Ursula) makes your ambitions futile. The key to every good team is that unless you open your pocketbook up regularly on this game, be prepared to make do with whatever you get. A couple good units coupled with a couple free units is the way to go until you start building a strong unit reserve.

Free units are sometimes the best for rounding out teams. I use GHB units in my horse and flier teams, and BK is a cornerstone of my armor team. Couple that with solid summoning and you can do anything without spending a penny. Of course, the summoning gods are not always kind. So make the best with what you have.

For now, you have very strong units. Build them and then formulate your teams to your liking.

I would start with infantry. The infernal GHBs often feature anticavalry units, making those somewhat more difficult to pull off. Doing the flyer and armor challenges without the limited editions mage units is tough too. Dragon emblem for infantry is basically a cheat code in most of these.

Infantry has a lot of options but Nino with good support buffs and Nowi would be top picks.
Flier: New Year Camilla, Cherche, Cordelia and a flying tome if you get one. Camilla's fast and bulky, Cherche and Cordelia work well with brave weapons.
Cavalry: Xander, Reinhardt, Cecilia, Lyn. Xander as a distant counter tank, Reinhardt and Lyn sweep, Cecilia with TA Raven combo to kill opposing bows and blues.