I would be happy to help. As far as crime is concerned I would check with the local police department. Here is a link to their website. http://www.colliersheriff.org/Index.aspx?page=1922
I would be happy to e-mail you properties that may interest you. In the 50k range you will not find much. I'm not sure where you are seeing homes for 50k in Naples, it may be from a site displaying inaccurate information.The best place to see what is actively on the market is with a Realtor. I would be happy to e-mail you listings, no strings attached and I won't pester you. If you would like me to set it up just send me what you are looking for and your e-mail address.
The closer you get to the beach, the higher your price point will be.
Have you considered other areas close by like Fort Myers or Cape Coral? You can get a little more bang for your buck. Cape Coral was voted the second safest city in Florida.
Please let me know if I can help email@example.com 239-209-2237
Have a wonderful day,