I live in your connection city (PHL) and we have a place in Sarasota (SRQ). My comments are based upon 6 to 8 roundtrips a year PHL/SRQ. I am also thinking you will typically connect in Philly. We have not yet chosen to leave a car in Florida, so we rent one. I typically use Hot Wire's value pick.
SRQ is a pleasant smaller airport. From PHL, the only current non-stops are on regional jets Friday to Sunday. And they are expensive.
The best and most economical solution for me has been to fly into Tampa and rent a car there. TPA to Sarasota is a relatively easy drive on the interstate which lasts about an hour. The car rental process in TPA is also easy with a new rental center you access via a modern shuttle train (like DFW) which runs every 4 minutes. The airfare PHL/TPA is typically around $270 (not including Easter crush) while PHL/SRQ is around $460. Since there are 2 of us traveling, this difference more than pays for the rental car. Also, rental cars in TPA are typically 10% to 20% less than SRQ. Sometimes, local friends offer to pick us up or drop us off; I have also rented one-way, which is about $50 all in for mid size.
So much for economics.. If your company is picking up the tab, that's not so important.
The questions of convenience and timing come next. There are currently 6 daily flights TPA/PHL. And these are on real jets, not regionals. There are 3 PHL/SBY flights at about 3, 6, and 9 pm. SBY/PHL are approximately 6am, 9am, and 4pm. Flight lasts about an hour, all on regionals. There are 2 CLT/SBY flights. You could figure which routings are least painful for you.
But, in case of irr-ops, PHL is a 2:30 drive to Salisbury. At least you're not stuck. CLT is not really drivable.
If you have more specific questions, just ask them. Any change, even one for the better, is always a bit traumatic. As with most travel-related things, convenience and comfort are valued at different rates by different people.
Now the miles thing. I currently use a Citibank AAdvantage Executive World Elite MasterCard. (What a mouthful!) When I signed up, there was a 60,000 mile bonus. Although it costs $450 a year, you get Admirals Club membership (a $350 value) and all kinds of travel insurance, including trip cancellation, Global Entry reimbursement, rental car protection, early boarding on AA flights, etc. You can also sign up for another card with a $99 fee and a 70,000 mile bonus. Just be careful because, to receive the miles, you must spend $3k or $4k within the first 3 or 4 months. I got one, met the spend requirement, then got the other. After about 6 months, I had 130,000 miles, which I converted into a business class trip to Europe. But don't listen to me. See if what is offered is of value to you.
Finally, if you had status on DL, ask AA to match it. If you fly a certain amount of miles within a specified time, they match.
So, enjoy your new location. Perhaps we can meet for a drink on St. Armand's Circle one afternoon!