Old Type Bath Drain
I went through this planning process with a bath remodel two years ago, and was going to replace everything but the tub.
I'm really glad I changed my mind and took a sledge to the old tub. Your old tub will stick out in the brand new bathroom, and you won't be able to replace it later, without messing up your new floor and wall tiles.
Also, to update the drain in that tub, you'll need to unthread the drain fitting from the tub, and that's gonna be somewhere between damn hard, and impossible. With a new tub, it'll take you 15 minutes to put in whatever new drain fixtures you like.
For $300, replace the tub while you're doing this major project. I promise you'll be glad you did.