Decide if you want a kitten or a full-grown cat. Kittens are adorably tempting, but be honest with yourself about whether you'll be able to match that energy level. Shelters are full of loving adult cats who have a much harder time getting adopted. An adult cat will be calmer and quieter than a kitten, but may also have behavioral issues from its previous life. Adult cats may also have medical conditions you'll have to address sooner than you would with a kitten. Also, kittens often scratch very painfully; Decide if you want that.
Consider medical concerns that may come with a specific cat. If you have your eye on one cat in particular, ask about its medical history to see if it requires any long-term care. Would you be able to afford this cat's medical needs?
Even if the cat is healthy, consider its breed. Purebred cats from different breeds can have their own genetic problems to overcome. For example, flat-faced cats like Manx and Scottish folds often develop breathing problems.
Purebred cats are more likely to have genetic medical problems than non-pedigreed cats
Consider the amount of time you have for a cat. While a cat doesn't need daily walking like a dog, don't be fooled into thinking that cats aren't a time commitment. They're still active pets that need a lot of play, and affectionate companions who demand attention. You'll also spend time cleaning the litter box and giving the cat structured meals.
The average lifespan of an indoor cat is 13-17 years, so be aware that you're making a long-term commitment to a new family member.
Consider adopting a cat from an animal shelter. The cost is minimal considering what you get: a fully vaccinated, health examined, and spayed or neutered cat. Any “free” cat is ultimately going to cost you those things down the line, if you're a responsible cat owner.