There are a number of factors that need to be considered. The cost will be determined upon that. Here are a few of the items:
Permits - what are the permitting costs? Will the building codes allow you build on a patio or will it require piers or frost wall.
3 season will need electric, windows, walls and roof. Will the patio support the load of the roof with shingles, windows and lumber for the walls. Would you use glass windows or a weatherwall system?
4 season requires heat runs (is you furnace big enough), electric, glass windows, walls and roof. Same question for the load of the roof and walls.
Before you decide to DIY, you may want to talk with several contractors. A local homebuilders association, remodelers council, Angies List, Yelp or Google will help you find potential contractors.
Best of luck. I would love to help you out, but we are in Chicago and the commute would kill any profit we might make.
Creekwood covered a lot of valid points. Unless you are doing a pre-fab enclosure, these things can vary tremendously. Remodeling Magazine does a yearly cost v/s value study on project done across the county (http://www.remodeling.hw.net/2013/costvsvalue/division/middle-atlantic/city/pittsburgh--pa.aspx). I would probably reference sun-room as a starting point.
I understand that cost is an issue, but a good contractor can actually save you money in the long run. A firm that does Design-Build will be able to work with you and your budget, to produce preliminary designs all the way through final construction drawings/documents.
Two professional organization around the Pittsburgh area are would be the NAHB
(http://www.nahb.org/local_association_search_results.aspx?state=PA) and NARI (http://www.nari.org/pittsburghchapter/members.asp). We are part of NARI and one state south of you. Good luck.
well I was hoping to get just a ballpark figure but... Oh well.