I'd still recommend to get a weighted keyboard. Heck, look on Craigslist and see if you can get a good old upright or spinet for under $300. I'd prefer the second option you listed. A weighted keyboard is a necessity for any pianist, especially since you want to play classical pieces, so I'd go with an acoustic piano if I were you.
Digital pianos don't really sound like a real piano. I wouldn't get a digital they sound pretty fake. A real one would do best.Yep.