I always use
www.homeaway.com or
www.vrbo.com to search for houses. If you arrive at a house and there are bedbugs, I would imagine that you would have to call the owners/management company and try to find alternative housing. I always check the beds for bugs when I get to a home just like I would a hotel. For some reason, I am less paranoid about bed bugs in a home because they have fewer guests overall.
When you are searching, you will start to realize what amenities are important to you. For us, we want one en suite bed/bathrooms for every adult couple. We don't want to have to utilize pull out couches if we can help it. We want a pool and spa, TVs in every bedroom, and a game room is a bonus. You may have different criteria.
If you do a search for rental homes on this forum, you may find some that have specific recommendations for homes, but in general, most people search the two sites listed above.
I have tried to find homes to rent in the St. Pete area because I have family in that area and would like to be close to them for part of the vacation, but there really aren't any good homes in that area to rent. Any of the homes I have found are way more expensive than in the Disney/Orlando area and they don't have the amenities that you can find in the Disney/Orlando area (pools/spas/# of bedrooms and baths...). If you are going to be going to the Busch Gardens area and Disney, you may want to consider staying in Davenport. We stay in this home that is in Grand Reserve which is in the Champions Gate area.
http://www.vrbo.com/46990 I am a repeat guest and I get a discount, so I stay for about $1050 for the week including taxes and pool/spa heat, but I think it is probably $1200 for a week for non repeat guests.
The nice thing about this area that it is close to I-4 and you would be able to go West toward St. Pete or East toward Disney pretty easily. This area of Davenport is Exit 58 off I-4. Disney exits are 62-68 (it takes about 20 minutes to get to Magic Kingdom from here). Tampa is about 50-75 minutes away.
As for price, every house is different based on the amenities and location. Areas closer to Disney (Kissimmee - Windsor Hills, Windsor Palms, Emerald Isle, Indian Ridge), will be more expensive than Davenport which is a little further out.
Once you narrow homes down, choose 3-4 and contact the owners for a price quote. Once you get the quotes, you can narrow it down based on personal preference. Once you think you have decided, verify ownership on the home. This thread will tell you how to do that:
http://www.disboards.com/showthread.php?t=3077601&highlight=tax
Okay, this should get you started. I need to go to church. I will try to check back later if you have more questions.