Every management company and possibly owner is different. Some will take any information on why the eviction happened (loss of job, illness), etc. into consideration. Others only care about when it happened as far as how long ago. My recommendation is to either find a Realtor who specializes in rentals or spend hours scouring Craigslist for individual owners who may be a bit more likely to accept a prior eviction. Good luck!
With an eviction on your record it would depend on the owner and how long ago the eviction was. In my area there are people desperate enough to rent out a property and hope for the best. This type of landlord is rare and when you see the property condition that is normally the reason they are willing