In the last year we bought 2 new construction townhomes, which we are renting out. I did the tenant search and screening. It was a fair amount of work, at first, but we haven't heard a peep from one of our tenants since November, and the other since he moved in in March. Our rent gets directly deposited to our account each month.
We have a reliable handyman who we know we can count on for pretty much anything.
The key to finding a great tenant is tough screening. I posted our listings on Apartments.com, Trulia.com and Rent.com. Both of the tenants we ended up going with found our listing on Trulia, which is a free site. Apartments.com and Rent.com each cost money (I think for both for 1 month it was a total of $150). We did the credit and criminal background checks through AmerUSA.net. It was about $30 for the checks. Each prospective tenant who contacted me was asked to fill out the same screening survey. After the screening I made appointments to show a few of them the unit.
In this economy you will likely have at least a few applicants with spotty credit. We had at least 3 people who had recent bankruptcies on record. We rejected 2 of them, but the 3rd we ended up renting to, as he was able to give us 6 mos of rent up front, and prior to his bankruptcy (which was due to his ex-wife's spending), he had great credit. The 2 other bankruptcies seemed due to the applicant's excessive spending. We didn't take the risk with those.
Make sure you know the local schools so you can answer questions about where the kids would go to school. Maybe provide a list of nearby hot spots.
Things have been going so well that we are hoping to buy another property this fall.
Edited to Add: Yes, we could have hired a realtor or PM to do our tenant search, but this is an investment endeavor for us, so it didn't make much sense to part with $1500 so easily (the cost of 1 month's rent, which is the normal fee taken my RE agents or PMs). One thing that we intend to do after the builder's warranty expires is to purchase a home warranty for future appliance breakdowns. From what I've heard it is well worth the cost.