Originally posted by hcc You will not find a cheap, fast zoom with good IQ for that price. Full stop.
If you have limited finance, you should consider MF primes which are usually cheaper than zoom lenses.
Quite right. Cheap-fast-wide-zoom are mutually exclusive. The fastest cheapest widest good lens is the Zenitar 16/2.8 fishy prime. The cheapest widest decent zoom is the DA18-55. The cheapest widest good zoom is the Tamron 10-24, and it's still beyond your budget.
If you can do without quality, here's an experiment to try: Get a DA18-55/3.5-5.6 kit lens. Get a cheap used A-type 2x TC. Remove the element from the TC and re-install it REVERSED! Your TC is now a 0.5x WC, a wide-converter. The kit lens becomes a 9-28mm f/1.7-2.8 zoom! WOW! The trick is to get the TC/WC element placed exactly right. Good luck.
Otherwise, get the Zenitar.