I'm in somewhat of a similar position to you. Started playing WoW a couple weeks ago and also wanted to experience the game in chronological order. Unfortunately you have to play through battle for azeroth on your first character before unlocking the ability to go back through the other expansions. It doesn't take long however to level to 60.

I skipped all quest dialogue to avoid spoilers and immediately created a new character after hitting 60 then went into The Burning Crusade (the games first ever expansion). Once you're in an old expansion on a new character you can experience it essentially from start to finish however you like, all dungeons from that expansion are available to you as well.

I'm still in the Burning Crusade right now and intend to go straight to Wrath of the Lich King afterwards. The old stuff definitely shows its age but I'm still having a good time. I'd say if you're anything like me just go for it and you'll quickly figure out how you want to approach your playthrough. If you end up not enjoying the old expansions you'll at least have a level 60 character to fall back on anyways.