Randall, Tomatoes are generally self pollinating, so in general, a large type tomato will breed relatively true to type, if it truly was an heirloom / open pollinated type. Small tomatoes like wild tomatoes, cherry tomatoes, current tomatoes are more likely to cross, so even in heirlooms for those you can have some different tomatoes showing up when you grow them out. If they were hybrids, the seeds might not replicate the parent tomato.
So in a nutshell, if you love the tomato and it's an heirloom and not tiny, it has a decent chance at coming out same or similar to the one you have.
(I'm sure KYH will correct any errors I've made...)
Some other vegetables, like squash for instance can cross pollinate for distances like a quarter mile, so something like a squash wouldn't be a good candidate to grow from seeds from one in the store you liked, but tomatoes are worth taking the chance.
I like to "clean" the tomato seeds, by fermenting tomato goo, then everything molds off at the top, and cleaned seeds come out the bottom. Kinda unpleasant to have around... you can just dry them with their goo and plant them like that next year too.
I'd think coming from Whole Paycheck, they're not irradiated.
Good luck.