We’ve been using Enterprise on our recent trips and it too has an office at San Justa. Which agency you choose shouldn’t make much of a difference. Personally, I stay clear of local only rental companies and stick with the major agencies.
Depending on the route you take to the small towns, you may never get onto an autovía (Autostradas are what highways are called in Italy, not Spain). A toll highway in Spain is an autopista. The main road heading south from Sevilla is the AP-4 and it’s a toll road. Since you have a few days, I recommend avoiding the autopista and take the smaller back roads to get to whichever towns you want to visit. As the distances are short the additional time it will take won’t be much and you’ll get to see countryside you’d otherwise miss.