I think it depends a lot on how much you know, how much work you are willing to put in, and how long you are willing to wait for the right deals to come along.
13 or so years ago I got my first 914 after reading as much as i possibly could. I bought to soon without looking around and in the long run got screwed money wise. It was not a looker by any means but had suspension upgrades and supposedly a rebuilt 2L. Motor dropped a valve seat within the first 500 miles, tranny was junk as well. Was into it close to 10k within the first year.. and that was 13 years ago. Good learning experience though.
Fast forward a bit to 2007, been working on 914s for a while, owned a couple parts cars and know these things pretty much inside and out. Guy at a PCA autocross has a grey 914 he got from his brother that he tells me he is just to tall for. 73 2L with FI, hell hole has been repaired, and documented 30k miles on a rebuild. Shifts better then any 914 I have ever driven. Picked it up for $3250. Have used it as my daily driver when the weather is good for the lat 5 years and spent nothing on it other then oil, gas, and the set of fuchs I got for it last year. Even passes emissions testing every year with no fuss. right place right time on that one.
Working on a lilac car for my wife now. When it is all back together I should still be around 5k. $1500 for a 72 1.7 car with a strong rebuilt motor/ side shift tranny, but questionable rust/rust repair. $1000 for a 72 non runner that had been garaged since 1986 with a solid chassis. Strip the good chassis to the bone, $1000 to get it painted (cheap job but looks great). Now its just time putting it all back together with the best parts from the pair of cars and another $500-$1000 in replacing all the rubber seals and it will be the most solid 914 I have.
Might be a bit tougher where you are at, but I think it can be done. Just find someone who really knows these cars to point you in the right direction. You will probably have to find something in your local classifieds or know someone though. People on the boards generally know a good deal and snatch them up quick.
Pics to drive the point home
I have under 5K in each of these
Click to view attachment