You don't want to bother looking for apartments during peak tourist season if you can avoid it. You can find a place, but it will be more difficult, and the search will be more frustrating. Instead, aim for an off-season apartment hunt. After August and before March is a good window to look.
When you're renting in Sanford, do your best to try and stay out of overly tourist-oriented districts unless you happen to be working in that area. Living in a tourist-centric location for long periods of time can be difficult. It is better to find a residential neighborhood more focused on permanent residents if you're moving to the area.
The Lynx system is the local public transportation provider. However, Sanford is by and large a car-focused city. You will find that most of the residents drive, and it is typically the fastest way to get to almost any given destination.
There are several smaller parks in the city, but if you want to truly feel like you're getting back to nature, visit the Lake Jesup Wilderness Area, which spans more than 490 acres. For some local history, visit the Museum of Seminole County History. Several operators offer airboat tours of local waterways. The Little Fish Huge Pond bar is a great place to take in live shows and grab a drink.