A higher difficulty will definitely have a lot more tactical challenges, but the hard part is knowing if you'll have fun solving these puzzles. My suggestion would be to find out for yourself and start a new game on maddening. Chapter 3/4 will give you a good taste of a "midgame" hard experience. If you find yourself enjoying the game, stick on maddening until you're frustrated, you can always turn the difficulty down. If you nope out at chapter 3/4, you still have your normal file.
Playing on maddening/no dlc myself and I think the gameplay/map design is quite good. There are significant challenges I can foresee on normal, especially if this is your first fire emblem and you don't have too much SRPG experience.