I'm new, but I was just wondering how much does it typically cost to sway an average player that lives within 100 miles.  I just need a generic base number. I have a budget of 3,800 and if I do future scouting of my home state, Pa, budget bumps it down to 2,200.  I only have 1 scholarship.  Is this enough to try to recruit a couple players.  

2200 is plenty in D3 to sign a player you just have to be careful. There are some really good guides you should read as a new player

One is How to win at D2/D3 by AEjones, another is a recruiting guide for new coaches written by me.

AEjones post is better, but you can find my post on page 2 or 3 of the forums right now so it'll be easier to find. Be sure to read up and understand how recruiting works, the good news is with only 1 scholarship even if you do poorly you can't mess up your team too much.

To answer your actual question, if you avoid a battle you can sign a player for pretty cheap. A campus visit and scholarship generally does the trick as long as nobody else is after him.

You can sign someone as cheap as 110 bucks with a promise and a scholarship but I wouldn't make that your strategy. 

Also: here is the guide I wrote a few years ago, take the time to find AEJones post as well he is a very successful coach who wrote a guide of how to win.  http://www.whatifsports.com/forums/Posts.aspx?TopicID=437944&TopicsTimeframe=30

I normally move to Div-2 fairly quickly because I hate the limited funds at Div-3 for recruiting.

At Div-3, you should be able to find plenty of players who will grow to be good so don't get "married" to a guy and think you have to have him ... there is usually an undecided guy who is almost as good just waiting to be signed for all but the absolute best players.