After starting Tharica 776 seven months ago, I can finally say I beat that game.
There are a lot of intense chapters that get your heart racing, my favorites are chapter 6(the ch. you escape prison) and 9(Escape the castle and Evyel is turned to stone) I think.
I'm pretty sure those are chapters 4 and 5, respectively. I'm pretty sure chapter 4 is a favorite of many who play the game. Besides that one, I really enjoy 14, 19, and 20 personally (if I remember the chapters correctly).
What are some old-school FE games I can get into? What do you guys recommend?
That... Really depends. A lot of the old-school ones are good, and it depends how old-school you want to go. The oldest I'd recommend is my favorite in the series, FE4, Genealogy of the Holy War. That game has the biggest maps in the series hands-down, but allows saving at the beginning of each turn to make up for that. It's a lot more forgiving than a lot of the older ones if you want an easier one (none of the old ones are a cakewalk though, especially the first time through.) FE5, Thracia 776 is an entirely unforgiving game if you don't know what to expect going into it, but if you're like me you'd love the challenge. Although admittedly FE5's plot would make more sense if you play 4 first, it's by no means necessary to do it in that order. If GBA falls under your old school category, they're all pretty good. FE6 has a pretty tough hard mode until the first arena, but normal mode is sensible. Still the toughest of the three GBA. FE7 has 3 different stories, which is cool, but the level of tutorial in that game always bugged me way too much. (Like seriously, I know how a promotion item works, so no, I do not want to promote Wallace right when I get him and screw him out of 8 levels IIRC.) But don't take my word for it, I seem to be the only one in the world who isn't in love with FE7. FE8 is on the easier side, but has branched promotions which is cool and my favorite desert map in the series, so that definitely counts for something. Also has an overworld map similar to Awakening, so it's the easiest transition from Awakening, IMO.
Basically anything from 4-8 is definitely old-school, but they're all really good games. I'm a big old-school FE fan, so I'd say those are all worth a look, but it depends on what you want in the game.