I disagree, the center isn't really necessary all the time. Especially if your L/R speakers are fairly close to the TV. I have gone with a 2.1 system (L/R + sub) several times over the years, and it's not really a big deal. (Just make sure that your receiver is set to disable the center channel, so it sends center channel sounds to the L/R speakers!)
If this is the case (i.e. L/R close to TV, and receiver set properly), then the sub is probably a better "bang for your buck" upgrade than the center channel.
It's not really a big deal either way, though, considering that all of this will be happening over a period of 6 months or so. Not so long to wait, either way.
You could also use your old HTIB speakers with the new receiver, in the meantime.
To pull this off in a real "budget" manner, I would recommend trolling your local Craigslist, especially for receivers. You can find basic 5.1 receivers from major brands for $100 or less. Just get one of those to start with, then put your money into the speakers, and then once you have all your speakers decided, buy a new(er) receiver with all the bells and whistles.
Just to give you an idea of what's possible.... My home theater is comprised of a THX Select2 rated receiver (Onkyo TX-SR705, $250 on CL), THX Select rated speakers (Atlantic Technology System 270, $100 from pawnshop for L/C/R, $50 from CL for surrounds), and a kickass sub (SVS 20-39PCi, $225 on CL). So for $625 I have a super badass system. Yes, it took literally a few years to pull all the components together (I got the AT L/C/R 4 years ago, then the receiver about 3 years ago, then the AT surrounds about 6 months ago, and the SVS sub last month) but IMO it's the best $625 system out there, by a long shot. (and I was being super picky with what I wanted; you could easily do this more quickly by not going after rare speakers like the AT's.) And of course I have been using the various components with other pieces along the way. I was using the L/R speakers as part of a stereo music system for a couple of years.... the receiver was driving a set of Polks. It didn't really all come together until I got the SVS sub, which is just SO much better than any sub I've had in the past. And now... it's blissful