Those fingers are gonna stay sore for a bit.. but it will wear off... before you know it, you'll be able to sit down and strum for a few hours at a time.
I run extra light strings on my acoustic.. I don't play for anyone other than myself so I don't need to kill my fingers with the steel... and with my arthritis is helps out a bit too..
The electric is your best bet if you're wanting to get a variety of play styles in too.. You can always go cheap for practice to get the handle on both... I don't mind playing my $20 Acoustic (was bought used from a friend of my son's) to get my finger picking down and watch Lisa beat me with her challenges with the going faster on the practice on the finger picks. :D And the $70 Strat I got at a pawn shop got me through tons of songs to learn here as well..
It's when you decide that it's time to start SOUNDING like your bands that you want to learn that you will start getting into the expenses... Pedals, Amps, and even the guitar's setup will start hitting ya on the wallet...
BUT, in the long run, it's worth it in my honest opinion. I've finally gotten some nice tunes impressing my son.. he came home one night from work this past week or so.. I was practicing Metalica's Enter the Sandman.. and he was standing behind me jamming out :D I caught him.. priceless..

Howard