Get yourself a Ruger MKii slabside or Government Target pistol
Get yourself a Ruger 10-22 or a S&W 15-22
Get a S&W 686 6" or a model 14 6"
GP100's and Buckmarks are reasonable alternatives
Shoot .22's and 38s for a while, in a year or so you will know what you want.
Each of those guns can be had used in good condition between $400 and $800
Set aside 1k to get your reloading setup for 38's
Join a local club and volunteer to help with shoots and such
You will meet great people who are happy to help you learn safety and basic skills.
Sit on the rest of the funds until your knowledge level gets up to speed.