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My halfling has the Fleet of Foot trait for 30' movement, and rides a dog with 40' base movement. The mount cost me 150g (actually 1 prestige point in PFS), and is workable with a minimum investment in Ride. If you want the mount to perform in combat, then it's worth consulting the Mounted Combat section of the CRB. Mounts do not scale up unless they are class features, so they will get pulverized at higher levels if you just ride one into battle.
Either purchase a pony (combat-trained) for 45 gp or a riding dog for 150 gp (you should get a copy of the Adventurer's Armory for that). You want a combat-trained animal like those so they're not spooked at the first sign of battle. The riding dog is expensive but has a decent attack and free trip ability plus scent tracking.
Next, you need a saddle. A normal riding saddle is 10 gp but I recommend getting the military saddle for 20 gp for the bonuses.
Don't forget to buy food if you have a riding dog. Ponies can graze but dogs like meat. The Animal Archive has carnivore feed for 5 cp/day. Each day's worth of food weighs 5 lbs.
Five pounds of meat? That's crazy! Oh well. Throw the feed into some saddlebags and let the pup carry its own food.
You'll want to protect your investment with some armor. Masterwork studded leather barding should cost 200 gp for a riding dog or pony and won't restrict your mount's movement or attack bonuses.
Spend prestige points to hire a porter. Have him carry the dog's food. Since the porter has no stats in PFS, he cannot starve to death and thus needs no food. :D