I do not recommend getting a really old horse or a really young horse as well. Old horses can have a lot of health issues that you may not notice at first and you want your first horse to be with you for a long time! I don't recommend getting a horse that isn't fully grown because you don't know if it will turn out funky looking or poorly proportioned. Look for trainability and I horse you get along("click") with.
Never to early to start. You should start by writing down criteria of what you are looking for in a horse (don't be too specific about colours and markings) and your budget. Them start looking. The looking process may be a bit tedious but perverse.
A big thing is make sure that you catch and tack up the horse and look at the living conditions when looking for a horse. Also take a trusted senior coach (no matter what level you are) to give you more advice on the horse. Also take a vet out for one final check. (You should test the horse multiple times)