Ignore all stories about Limerick, it's a great city, a young, vibrant student city. Most of the "trouble" stems from 2 waring families, other than that it has the same if not less crime that any other city in this country. I'm from Limerick, never seen any trouble. My family still lives there.
Regarding where to live, the following areas are great:-
Out the ennis Road direction (north)
North Circular Road (expensive)
Clareview (close to NCR - good area)
Greystones (adjoining Clareview)
Lansdowne / Farranshone (all close to above)
All above about 20 mins walk to city centre
Castletroy (situated on the way in the Dublin road) - close to the main university - good area, quite built up over the past few years though. Alot of students.
City centre - South Circular Road, alot of recent development - very nice area, walking distance to centre.
Any of the above, my preference would be out the ennis road, NCR to your left - Greystones / clareview to your right.
Best of luck with your move, I'm sure you'll make it a lovely home.
Kitten