Ok, that gives me a lot more data upon which to make some forecasts.
First of all, you are very likely correct in expecting your incomes to rise. Madison's pay rates generally are higher than much of the rest of the state, largely because unemployment is so low (around 2%) that employers have to pay premium wages to find workers. The downside to that, of course, is that it drives costs higher as well, and you can definitely expect to see an increase in your cost of living if you move here.
I am not in the IT field, but if you have a degree in computer science, even as an entry-level software developer, you should be able to land something that'll earn you more than the two of you make together in Virginia. And a good administrative assistant working fulltime should be able to pull in somewhere in the $20-$25K range.
Warning: I am glad that you have some leads, and by all means follow them up, but don't be too surprised or offended if you don't land an offer until you actually have a Madison address. A lot of other people who post to this forum have reported very little interest on the part of prospective employers when they apply from out of state, a situation that changes dramatically once they're finally living here. As a hiring manager myself, I can understand the employers' point; when you need to fill a vacancy, you'd rather find someone who can start in two weeks than someone who'll need two or three months to get relocated here, and who may want moving costs covered to boot.
So let's assume that you're in Madison and you're looking for a place to live. This is going to involve some sticker shock, I fear; your $700 place in Virginia could cost you as much as 50% more here in Madison. That's the downside I mentioned earlier, and it kind of sucks, particularly when you're trying to relocate on the wages you're making there. If you wanted to live anywhere near the UW campus (which I do NOT recommend), that same apartment could be as much as twice the cost of what you're paying in Virginia, with parking an extra $75 or more on top of that.
Don't let that scare you, though! While I would not try to claim that anywhere in Madison is "affordable", the east side probably comes closer to that than most other areas. You can find places in a similar price range to your current apartment, although probably not with the same amenities, and most areas on the east side do not charge extra for parking. This website:
Start Renting - Search for your Madison, Wisconsin Apartment is a good place to start.
As to utility costs, that can vary so dramatically that I won't even try to quote specific numbers; the range is just too huge, and it wouldn't be any use to you. However, once you find an apartment you're interested in, you can go to
Average Energy Use and Cost for Residential Addresses to find out what the past year's worth of gas and electric bills for the place have been. And for comparison, you can check other apartments in the building or addresses on the street, to see if the place you're looking at is typical of the area.
As I've suggested to many others on this forum, you should always check with
Tenant Resource Center before signing a lease in this city. They operate as a sort of Better Business Bureau for landlords, and can tell you if your prospective landlord is a good guy or a slumlord.
Your thought to settle for a less-expensive, not-quite-ideal place for 6 to 12 months is a good one, too; we did exactly that, and found that it gave us the time to house-shop more carefully. There are several large apartment complexes out near East Towne Mall, which, while I wouldn't buy a house out there, wouldn't be a bad place for a short time.
When you do go on the market for a house, you'll want to spend some time here:
City of Madison: Assessor's Property Information to find out how much those property taxes will add to the mortgage bill. They can be pretty spendy, I'll warn you. At the same site, you can also see how home prices are in a given neighborhood or on a particular street.
Another thing that I'd suggest is that you go on a typical grocery shopping trip there at home, and keep your list when you're through, along with your receipt. When you visit Madison, take that list to a couple-three of the local grocery stores with a calculator, and see how much the same basket of groceries would cost you here.
If you have a vehicle, you might also visit a couple of different local insurance agents to get quotes on how much insurance will cost you here. That can vary enormously from one state to another.
You don't mention whether you're childless, have daycare-age kids, school-age kids, college-age kids or are empty-nesters, but obviously all those variables will factor into your costs as well. You'll want to check in with daycare centers and after-school-care centers here, if that's relevant to you, to see how prices compare to what you pay now. Since our offspring were in their teens when we moved here, I can't tell you what to expect for those costs, but a few phone calls could yield you plenty of data.
Good luck! It takes time to do all that research, I know, but the better you prepare yourselves, the likelier it'll be that your move will be relatively easy and the transplantation process a success. We'll watch for you at the Farmers' Market!