Unless you have a lot of experience with horses, you don't need a stallion. Stallions can be difficult to control, especially around other horses, and can be dangerous when an in-season mare is in the area. If you're serious about getting a stallion, talk to experienced horse people and find out what they recommend. Stallions of some breeds have calmer dispositions than others, but you don't want to buy a stallion and find out too late that your horse is the exception to his breed's calm-stallion rule.
A mare is much better for the average horse owner. While a mare can be a little irritable while in season, it's rarely a problem, and you always have the option of having your mare bred. If your horse is a well-bred animal with no conformation issues, and particularly if you show her, it makes sense to breed her. On the other hand, a mare can be much more expensive because you're not only buying her, you're buying her future foals as well. A good broodmare will never be cheap.
If money is a consideration, or you just don't want to deal with foals, you can always buy a gelding. These neutered males are as even-tempered as mares and may be more predictable in behavior.
In the end, the choice is up to you. Just be sure to do your homework before you decide on a stallion, and if you choose to breed your mare make sure you know what you're getting into.
What age should your horse be?
A younger horse generally has more energy than an older horse, but may also be more excitable, nervous, and harder to control. An older horse is usually calmer and has a less changeable personality--young horses, like young people, sometimes try out "attitudes" to see how they like them. An older horse may also be better trained--or then again, it may have more bad habits.
Unless you have experience training horses, you probably don't want a very young horse (under six years old). Often, a "green-broke" or novice horse will sell cheaply, but it takes a lot of time and effort to finish the horse's training. Then again, if you have the time and experience--or an experienced trainer to help you--finishing the training can be a fantastic way to bond with your horse and also get him or her trained exactly the way you like.
On the other hand, if you buy a very old horse you may be buying some physical problems as well. Even if your vet pronounces the horse sound, will he or she still be sound in a few years? If you just want a horse for non-strenuous rides and companionship, though, an older horse may be ideal, and you have the added satisfaction of giving an old-timer a good retirement.