I'm 15 years old and just beginning to play cricket. While I was researching bats I decided to get a light weight bat (around 2.6 lb) - but how do I find out what size I need or what company bat I need?
If you have a sports shop near you that stocks cricket kit, go there and examine all the bats. Lift them, handle them, see how they feel in your grip. Find one or more than feels right, picks up well, has your preferred weight etc.
When you find one or more that you like, examine the prices. See if you can afford your favourite, or see if you can get the same bat type online within your budget.
I would encourage you to buy from the local shop though, if you can. That keeps them in business.