For the light rail, you'd still need to take a PATH into NYC (from the Pavonia/Newport stop), but it'll still be faster than taking the 99S (express bus to Port Authority) or the #10 to JSQ. Also someday in the future they're going to be adding a stop to 8th st. depending on if and where you moved to Bayonne (currently it's 45th st., 34th st. & 22nd st.. Of course, seeing as I live on 10th st. currently, they won't have it up and running until after I move and no longer take the light rail to work. :| /rant)
Honestly if you're looking for quiet and safe, Bayonne is a good choice. Actually, it's almost so safe and quiet sometimes it seems like the entire police force will come out just for a speeding ticket.
Looking through today's Community News, most 1 bedroom apts are going to run ya about $800-$950. They're also building tons of condos but I don't know about those prices.
Also Bayonne has it's own
webpage.