The cheapest run is the one you make with scrounged (or deeply discounted) materials. So, I'd look around and see what you can find in the way of wire mesh, and design around that. If you have farm auctions in your area, they are often a good source of affordable fencing, even if it is sometimes used, or try craigslist, freecycle, etcetera.
I would suggest at least 6x10 for four hens but a lot bigger is a lot better, esp. if you want more in the future. Remember that putting a wire or roof-type top on it is the only way to get really thorough protection against climbing predators such as the ubiquitous raccoon (for hawks, you could just drape netting or string strings across) BUT will require a good bit more material. With or without a top, you'll want your run to be like 5-6' high -- with no top you'll need the height to discourage chickens from leaving, and with a top you'll need the height so you can get in there and work/clean/etc.
Once you have scrounged your wire, you will know what exact size your run will be
I strongly strongly recommend setting 4x4 pressure-treated wood posts for the corners; t-posts are vaguely adequate as line posts but will not last well for a tight solid fence if used as corners. Set your posts at least 3' deep.
Good luck and have fun,
Pat