I think that depends on the niche of your forum.  Some niches are better paying than others in the context of ppc advertising.  I wouldn't expect much return in the first 3 to 6 months on a forum.

PPC returns are notoriously poor for forums unless you have a very busy forum in a preferred niche. 

Back to the original question by the OP.  It varies a lot and is dependent on your niche.  You might wish to put out $20 to $40 for paid posting while at the same time running a two week AdWords campaign and also targeting rival forums in your niche with  daily link drops.  This should help build a head of traffic quite quickly and for in the region of $100.  Getting that money back will not come until you get enough regular daily traffic to offer value to potential advertizers. Text link ads might be your best option to recover the money quickly.

In addition to what people have noted above, affiliate programs are also a good way to try to make a little with forums.  It is true that PPC is not always a great earner on forums (although there are many exceptions where PPC does pay nicely).  Commission Junction (cj.com) offer a number of affiliates for most niches including eBay as an affiliate program. 

I suppose it all depends on your niche.  If you are a connected with a classical music shop, then, naturally, you do not want to shoot yourself in the foot by advertising your competitors.  In this instance text links might be better or something non-contextual, or some ad scheme where you have a greater degree of control over which ads appear.

Are you using the forum to draw in potential shop customers?  Or are you trying to create a separate business entity from the forum by directing shop traffic to the forum?

If you can track how customers found your online shop and then discover that some of them found the forum first and then went on to buy from the shop, then I suppose you could argue that your forum is already beginning to show some return.

you can do it that way but it might not be too accurate because not all users will answer the poll. the best way would be to analyse your web server log files to see who the referrers are.

The amount you spend and for how long is depended on the competition for your niche. If you are competing for members in a niche that is super overcrowded, you will have spend a lot of money to convince them that you forum is better than Joe's who they have been with for a year. Paid posters, advertising, buying links and building your forum all takes time and money. I worked with one guy who got into a MySpace related forum a he spent hundreds of dollars and almost 18 months before the forum took a life of its own. He ended up making his money back quick with Link sales and ended up selling for a huge profit. It can be done but it may take a lot of patience.

Assuming the only thing you spend money on is promotion and possibly designs and mods, then I would say you should see a return on your investment almost immediately, in traffic that is.  Getting the people in your forum is the first part, making money with the forum is the second part and completely different as far as I have seen.  I have experimented with adsense but have not made that much.  Maybe if I increased my traffic that would change.  I am going to test textlinkads.com because I think that might sell very well if you have a lot of traffic.

This is great advice in my opinion. Don't spread your advertising budget money over too much time.
I think if you pay a few people to post in the beginning and spend money elsewhere to promote your forum then you will gain quite a few members in the beginning and you could possible see a return on your investment within 1 - 3 months.

Good luck!