Yeah, I'd focus on making sure that it's a quality product (i.e. not Acer) and not overpriced for what it is (i.e. not Apple). I would personally look to buy something with a 64-bit system and at least 4 GB RAM for about $300-$500, and read reviews online to make sure that it doesn't have any problems related to things like the fan or other hardware the computer has but isn't usually mentioned in the specs (mostly, you can stay safe in that regard by not buying Acer). For instance, my parents used to have an Acer laptop which had a fan which had an unusual tendency to get dirty and so full of dust it would cause the computer to heat so much that the touchpad would start clicking on its own (as a side note, I swear half the stupid things I did on Facebook as a teenager was really just that touchpad doing whatever it wanted while I was afk), so avoid that kind of stuff.
Also, you should look up CPU benchmarks on Google and compare them with whatever experience you have had with previous computers to give you some kind of an idea whether or not the processor is good enough, but most modern processors can probably handle all of that stuff just fine. Also, depending on how much extra you would have to spend and how much you care, it might be a good idea to buy a laptop that has, say, 4 GB of RAM but it can be upgraded to 6 or 8, or if you want to cut on the expenses instead, you could buy a laptop with 2 GB of RAM that can be upgraded to 3 or 4 — doing it that way is generally a lot safer because you're not risking overspending on extra RAM you don't really need, and you're not risking buying an entire laptop that isn't good enough for your purposes.