Indecision

If you are aiming for Teir 20 then Mergeability is a must.
So everyone in the choices are good choices to begin.
IMO go with Hana cause She is easily obtainable and is really really good. (and maybe Raven with the same reason as hana)

But If you are'nt aiming for teir 20 then I recommend to go with Nanna cause it seems you need more healers and Nanna is Really really good with her Assist.

It's between Raven, Hana, and Shigure.
Raven outclasses Linus on Player Phase and has a crazy amount of power, but you might want to wait for a +Spd Raven. Also worth noting that if you don't have enough Divine Dew, you should probably wait to build Raven.
Hana also has a crazy amount of Player Phase power, but for what it's worth +Spd would be better than +Atk for an FSweep set.
Shigure has optimal IVs and is arguably the second best lance Flier in the game. I would only upgrade him if you have an FSweep lance ready, though.
tl;dr, Shigure if you have an FSweep lance ready or need a Player Phase Blue.
Raven if you need a second or stronger Player Phase Green, as he still works with +Atk very well.
Hana if you really need a Player Phase Red, because she really wants that +Spd.

I'd suggest Felicia as she is an excellent anti-mage unit. Her plate more than makes up for her relatively low attack as she always hits the lowest of Ded/Res while her refine lets her get off repeated Glacies. It's fun watching her destroy an armor unit.

Shigure is your best bet. His kit is mighty good even without investment, having the wo dao effect, and rapidly proccing moonbows can be hella effective

If you don’t have a sure-fire way to take out green armors, then:
(Hana) is the best choice from a budget perspective. You can inherit the Firesweep and use her that way while kitting her and her support for speed, and also forge her native Armorbreaker sword for +atk and make good use of her IVs as an alternative anti-Armor build. Because of her min-maxed stats and color, she can function well at low merge levels, but will excel at higher levels (which is easy to achieve).

(Shigure) is the next best choice, because he can also function as both player phase and enemy phase due to his spd and decent def, + being a flyer to use flyer—specific movement support, giving you a lot of ways to use him in different teams.

The rest are all too niche to justify 5* if you’re a budget player (in my opinion), but you can make most of them great with enough investment.

Some really good choices here. I'd prioritize them like this:

1. Shigure - without a doubt, one of the best lance fliers. Very fast, versatile in his builds, and has a good weapon to pass if he ends up just warming the bench. Also a good alternative to Valter for his merge potential down the line.
2. Hana - again, shes versatile thanks to her speed. Some may argue Soleil is better but Hana has the slight advantage of ease of merge.
3. Nanna/Priscilla/Sakura (in that order)- healers are never a bad idea, and specifically cavalry healers are strong. Especially good choice to have more healers for Arena Assault.
4. Raven - seeing as you have Linus already I'd hold off on him. Linus already comes with an amazing starline and kit, Raven can be a better sweeper with a +speed IV though like someone else mentioned. Even then I think Linus is all you'd really need unless you wanted to merge Raven.
5. Felicia/Kaze - both are strong mage tanks, Felicia has the advantage of a legendary weapon but can't go wrong with either. Mage tanks are more niche but they're not bad choices either.
6. M. Morgan - seeing as you have plenty of red mages I'd hold off on him. I have to admit I haven't really used him, but tharja can fill a similar role already.

A lot of people were talking about arena potential. Is that one of your goals in the game?

The only recommendations I have are against certain choices:
- neutral Kaze. He hits harder than Felicia, but not quite hard enough to pierce the defenses of most melee units according to my estimations, and you probably won't need the extra atk against mages, which makes him probably just a worse Felicia unless you invest significantly in his attack. Even then he will struggle against DC units due to his low def, so you may as well go with Felicia and target their res. Also, you might like to fodder his atk smoke or even his dagger at some point.
- Raven, because you took Linus, unless you want to 5*+10 merge Raven. But consider carefully, as with any 5*+10, because that's a lot of effort and attention
- M.Morgan, because you already have so many red mages, many of whom debuff
- Sakura with those IVs. She is one of the best healers when it comes to tanking physical attacks (second only to Azama, if my memory is correct, and she's faster) so if you choose a healer I would take either Nanna or Priscilla. Priscilla has the better IVs (because HP is mixed bulk when you're fast enough) and worse fodder potential, so I would probably pick her over this Nanna if you decide to go with a healer.