Don't you have a chance to join a ukulele meeting somewhere near you?
This is usually a good occasion to see (and touch) many different ukuleles without having to buy any - this might help to get a better idea about the sizes and brands.
One point to consider for budget: there is a market for second hand ukuleles (even here on UU). Either try to get a better one for small money - or buy a better one first and sell it later (in case you don't like it) to minimize your financial loss.
This is usually a good occasion to see (and touch) many different ukuleles without having to buy any - this might help to get a better idea about the sizes and brands.
One point to consider for budget: there is a market for second hand ukuleles (even here on UU). Either try to get a better one for small money - or buy a better one first and sell it later (in case you don't like it) to minimize your financial loss.