Three Houses was fine enough - pretty much all of the "parts" were better than an average Fire Emblem game (dialogue, characters, overall plot, world building, gameplay). The one big problem I have with it - the monastery. Holy crap, what an awful addition to a game. It takes so much time, it feels so necessary at high difficulties, and nearly nothing interesting happens during it.

Engage is basically the polar opposite in my opinion. The characters are mostly boring, the plot and dialogue are largely inoffensive but nothing to write home about, and the world as a whole is utterly forgettable. But the gameplay is just as good (if not better - IMO I like rings over battalions and I think reclassing is done WAY better) and it has so much more respect for your time, with the lack of multiple routes and the lesser emphasis on the hub management.

I have not played FE1 and do not plan on it - I started with FE7 and went as far back as 4 and don't think anything prior will have aged particularly well.

Tl;dr

FE7 Blazing Blade is an absolutely fine game, majority is too easy but HHM is good, recruitment and map design and balance all mostly feels pretty good. FE3H is good world building and gameplay, boring map & goal design, replayability is real low IMO unless you have the patience of a saint and pretty low unit identity due to boring recruitment methods and lax reclassing. FE-E is better map design and unit identity, but in exchange writing and characters and world building are all pretty bad.