Ziploc freezer bags work fine for low temp SV, but it's important to buy the name brand and to make sure it's a freezer bag. And don't use them at higher SV temps (e.g., 180F+) where polyethylene will start to soften. I have never had one fail, and I've been using a circulator for over a decade. As mentioned upthread, you can exclude the air from zip-top bags using the displacement method. There's no better way to do it, though it does work better if you add a bit of oil to the bag along with your meat.
That doesn't really help the OP out though, because he's looking do to "cook->chill" and that's where you really need a proper vacuum sealer. The good news is that most of the cheap edge sealers work just fine. America's Test Kitchen likes the Nesco Deluxe Food VS-12. Chamber vacs are nice to have but aren't really necessary. If I was only going to do smaller portions (and maybe a small roast every once in a while, I'd probably go with the Anova chamber vacuum, which has a small form factor and looks like a great value. I've seen a few people who were happy with the smaller Avid Armor chamber vacuums too, which are also inexpensive. Part of me bets that these come from the same factory as the Anovas. Or at least the same neighborhood in Shenzhen.
I'll also add that it takes the same amount of time to reheat a chicken breast or steak SV as it does to cook it from raw. I didn't find there to be a huge time savings in batch cooking individual portions (if they were later served hot). There can be a real financial savings, however, if you buy in bulk on sale, vacuum seal, and then cook->freeze. But most of that savings comes from the vacuum sealing, not the sous viding.