When I take on a new student who is primarily coming from classical the first thing I work on with them is playing rootless voicings with added tension. This would be how to voice chords without using the root and adding tensions (9, 11, 13). I also show them how to interpret chord symbols at the same time. These two skills allow you to start reading from the Real Book and playing tunes that sound like a real jazz player.
The time it takes to achieve these skills varies but is usually not less than a year to gain fluency. Once you have your chords ready to go you are set to go in a bunch of different directions, like adding improv, learning other voicing techniques like solo playing or two handed voicings etc.
I offer a complete online course of study on all of these topics, please see www.jazzpianoonline.com.
I have four completely free, full-featured lessons for you to try.
As for the piano question: it looks like you can fit up to a 7' piano which gives you a lot of options. I would take advantage of every inch of that and look at these used Yamaha's: C3 (6'1"), C5 (6'5"), C6 (6'7"), or if you can fit it the C7 (7'6") which is the benchmark jazz piano. I just saw Rick Jones had one online that sounds really nice and is a great deal.
Steinways, in my opinion, are of course very expensive (over priced imo) and very inconsistent especially the smaller instruments and don't come close to the reliability and stability of a Yamaha. (any technician will tell you this). Yes you can voice any piano to yield the sound you are looking for just make sure you are working with a top level technician before they do any voicing to your piano because an inexperienced tech can do real damage to your hammers.