Buy it for Life

Honestly, I'd recommend against buying a cookware set unless you think you'll really use every piece in the set or it's too good a price, because manufacturers tend to bundle in something that you probably won't get too much use out of or is a bit redundant (like an 8 inch fry pan).

As far as brands go, most of them are going to be pretty similar at the entry level price points, so I'd pick based on how comfortable/attractive the handles are and whether the rivers are flush or not. I wouldn't pay much attention to 3 vs. 5 ply when it comes to different brands, but instead to focus on the weight and thickness of the pan itself. Generally, a thicker pan will sear better than a thinner pan, but will also be less responsive to changes in temperature (these will probably be minor differences except with something extreme like a Demeyere Atlantis, so don't get too caught up on this).

If you're looking to put the pans in the dishwasher, you might want to splurge for a brand with sealed rims. This helps to prevent delamination of the layers, which can happen in the dishwasher (see All-Clad lawsuit). However, this process does add quite a bit to the cost, so if you don't plan on throwing them in the dishwasher regularly feel free to save money by getting unsealed rims. The cheapest brand that I'm aware of with sealed rims is Misen, but someone please chime in if you've seen a cheaper one.