If AF is'nt important to you then I'd recommend a manual focus prime as they are generally sharper than zooms.
I dont think you actually mentioned how wide you want to go but 17mm primes go very cheap. I picked a Tokina 17mm f3.5 RMC up for about $15. The Tamron SP 17mm f3.5 is better but it cost me about $180.
Both are FF lenses.
If you want to go wider than 17mm on the cheap but dont want a fish-eye then the Sigma 14mm f3.5 is probably about as wide as it gets for a cheap manual focus FF rectalinear prime. Got mine for about $100. I really like 14mm on crop format as it gives the equivalent FOV as a 24mm lens on FF.
Here are some Sigma 14mm samples...All wide open and handheld:
If you want to go go wider than that on crop format, without resorting to a fish-eye lens, then you will need a modern AF zoom.
The Sigma AF 8-16mm EX is currently the widest rectaliner zoom on the market for crop format and its an excellent lens...But perhaps a bit over your budget in the price department.
The Sigma 10-20mm f3.5, again for crop format, is also excellent but again perhaps a bit too pricey.
If you want a really wide fish-eye lens for crop format then again, its Sigma that offer the widest available. The Sigma 4.5mm EX is currently the widest fish-eye lens with AF on the market.