Not easy to say. Android version is an obvious starting point and is much more important than with bigger names because with this cheap ones, you normally don't get any support and updates, so you will be stuck with the version that came with the tablet. Don't go below KitKat if you can afford it. Jelly Bean is the absolute minimum, never below that.
After having seen a couple of smaller tablets and related user problems, I'd say the second most important point is the memory. Cheap tablets come with smaller amounts of memory and while they usually offer a card slot, this can be very deceiving. Android only allows you to move apps between the first and second memory area (provided the app itself allows it, which is usually rare, so better not counting on it). And I saw quite a few tablets where the internal memory is already partitioned in two, the memory card coming in as third, for instance, a 8 GB tablet:
- 1 GB internal memory
- 5 GB secondary memory (usually named USB memory, even if that name is a bit misleading)
- your memory card, say, 16 GB
In this setup, you can't move apps to the memory card, only to the secondary ("USB") memory. And because most of your apps will not move at all, you're practically limited to 1 GB of actual app storage that is hardly enough for the standard selection of browsers, video players, Facebook and similar stuff and the memory card won't help you, either. The problem is, the manufacturer will not tell you this, they will simply state that you have a 8 GB tablet, 6 GB available. Which is, of course, true, considering that 1 + 5 = 6 but this doesn't reveal the whole situation.
Somehow you have to make sure that it isn't partitioned this way, that you will have at least 2-4 GB of real, app-usable memory to play with. The more the better, of course. But you'll need either personal testing or at least a reliable review somewhere where they describe it precisely enough. If you can check it out in the flesh in a store, that would really help.