Get a bass that is comfortable in your hands, and which sounds nice in the shop. Don't buy anything without trying it first.
It's worth playing a bit on a borrowed instrument, until you can at least play a simple bassline in the shop. That gives you the ability to know what feels right to you.
One of the first ways they skimp on cheap basses, is in the neck. It's expensive to construct a neck that can support the tension of bass strings. The cheap way is to make the neck thick and heavy. If you don't have large hands, that can be a big impediment to playing. You'll notice the difference immediately in a shop.
If you have small hands, a short scale bass will feel much easier to play. Some people dislike the more muddy tone, but it's subjective -- go by what you hear, not what people say.
If you're on a budget, and you're a beginner, it's better to have a good quality instrument with fewer features, than a low quality instrument with more features. So just one pickup might be a good compromise -- you can't fiddle with the tone as much, but you may have a better instrument to learn on.
Don't forget to budget for a half-decent amp too. Also test this in the shop. The amp is an important part of the sound creation. It's very unsatisfying to play bass without being able to hear the low notes.