Paladins were at their peak in FE9 but they haven't ever really been properly nerfed other than in dismounting games and FE10.
You will find Lyn and Eliwood aren't all that great in HHM, the former for having wet paper durability, and the latter for being mediocre all around until he's received so much favouritism that he's become good all around. This is possible, but not desirable for efficiency. Doesn't mean you shouldn't do it though, especially not if you want Geitz (and you do).
Lowen, Hector and Guy are all solid units.
Canas, you might find, profits a lot from that first Guiding Ring. I wouldn't say to give it to him as soon as possible (as it murders his EXP gain), but somewhere between 13/0 and 20/0, when his EXP bar is low at the start of a level. He'll gain 4 AS, which means he'll start doubling a whole lot more, and he'll also be able to Heal. He won't get more than Mend unless you actively try to get his rank up throughout the game, which isn't too great of an idea because Priscilla also needs leveling.
Pent is a great low resource unit. Louise is a niche unit, useful for situations which require Pent to take on a lot of enemies on his own. Carefully place her just out of enemy range, like in their joining chapter, while Pent is in range and using that +3 def to its fullest. She's also good for using high level bows, but you also have Geitz for that (he just can't use Silver), and Geitz is better in like every way. But if you don't manage to get Geitz, she can do things like using Longbow on Luna Druids.
Geitz is another low maintenance man that can do almost anything to you as long as it's not magical. Axes and bows have insane versatility and he's the fastest guy who can use both.
Rath is rather bad, and will be a pain to train, especially since around the time he rejoins you will be feeding EXP to Eliwood and Lyn to try and get Geitz before FFO hits. But, like almost any unit, he's usable. It's just that he's your third high-level bow user, so he's not going to add much. Good rescue/drop bot, though.
Priscilla is great. Hard to level up if you don't let her heal every single point and you finish maps as quickly as you can, though.
Heath is the easiest flier to raise barring Farina, surprisingly, since you can concentrate EXP into him for a short time and then he becomes awesome and durable. Still, it requires favouritism, once again taking off EXP you'd want to give to Rath or your lords.
Matthew is of course stellar. Give him some Lyn Mode EXP and consider giving both the Robe and the Ring to him, it makes earlygame a lot easier if he's in good condition.
What I'd recommend doing is dropping Rath, it'll save you a lot of trouble, and you won't have enough unit slots for all these units anyway. The other units are all fine.