There are a lot of potential tenants at the moment due to pressure on housing from recent migrants from the new EU states - so you're more likely to be inundated than have trouble finding someone. I tend to use the local paper for my house but online noticeboards like Gumtree for a house that we let out room by room.
I rent my own accomodation and have dont for years and agents treat tenants worse than they treat landlords, so bad agents are far more likely to lead to problems with tenants behaving badly as they feel that they owe them (your agent) nothing. The only thing an agent can do for you os a credit check - but I'm not really sure how valuable that is.
I think landlords tend to put down things like No Housing Benefits and No Students out of prejudice and do themselves out of really lovely tenants. My current tenant is a mature student in his 30s. No HB is a bit more understandable as councils can be slow to pay, but that does vary and HB tenants often stay for much longer than the 'working professionals' that most landlords seem to want. Better to weigh up people as they come.
I assess people carefully over the phone (I have a list of questions, but I also chat to them) and filter out lots that way. I always take someone else with me when showing prospective tenants round as the other person can pick up clues while you're chatting (and I did have one incident when man turned up at 9am drunk I wasn't going to let him in and I was glad someone else was there to back me up in case it got difficult). Despite being a total slob myself, I would always pick someone who's neat and tidy and it's important that you 'click'. Use a proper agreement (from WHSmith) and agree an inventory from the outset even if you're more flexible than that, it sets the right tone.
If you treat your tenants really well, don't go for absolute maximum price, repair/ replace stuff quick, and be friendly but make sure it's a clear business transaction, they find new tenants for you when they go, are OK about you redecorating while they're still there and understanding if there's a genunine problem getting something sorted. Treat them like cash-cows and they nick stuff, trash the place, you get voids, and less choice of new tenant.