Well perk-wise, if you wanna be stealthy you know your perks. Blind eye, Assassin, Dead Silence (Optional, I perfer Marksmen).
Also I like the 50 Cal, Silencer, and Reduced sway attachment. Thermal/Heartbeat are not very useful in my experiance. Too many people with Assassin for it to be super effective. I normally just keep my head on a swivel.
Now maps, I like to snipe on:
Hard Hat (hit and miss map, I keep watch on the pipe in the middle of the map)
Sea Town, another hit and miss map. Sometimes traffic is good, other times not so much.
Mission, you REALLY need to watch your back on this one.
Bakaara, I snipe on the helecopter. The smoke hides you for a good 5 kills normally.
And thats all I can think of, but really, most maps are not built well for true sit and wait snipers. Either it be the good sniper areas people avoid people they will get sniped, there are too many entry points to your sniper location to be overly effective, or the map simply is not built well for sniping. Hopefully the map packs will be a few more sniper friendly maps.
Personally I wouldn't use a silencer, it makes alot of kills become 2-shot rather than one shot kills, but you will give away your position (kill cams do that partially anyway)
but yeah for stealth, blindeye, assassin and well for sniping i'd definitley go for marksman, because if your going to snipe like this you probably won't move around all that much.
Maps I think are decent for sniping are: Interchange, Bakaara, Mission and Village. Outpost and Seatown are definitley snipeable maps also.
I like the Barret myself, standard scope, impact, Blind eye, Assasin, marksman.
Silencer is optional, but I normally don't use it. On these maps you have to move around anyway to avoid being killed after a few kills.
Bakaara is my favourite map, it has a few different good positions. i also like Fallen, though it depends on traffic a lot. Resistance is also good, across the alley at the bottom, but you have to cover the different entrances so it's hard to stay long in the same spot.
Seatown has some good spots, but traffic is always bad in my experience.
My setup is the L118A, with kick and extended mag as primary.
secondary is akimbo MP412
I use bouncing betties and concusion.
extreme condiontion pro
The L118A has a great scope, it goes preety far, and for the most part is 1 hit kill. Kick is important with extended mag incase you miss you can get another 1 or 2 off before they flee.
Akimbo MP412 is what pisses most people off. Six rounds in each pistol, reloads fast, and has the most damage for a pistol. You can shoot off 12 rounds in 1 second accuratly.
I rarely get a kill with betties, i use them as enemy detectors, if it goes off i know someone is close, get out my pistols, and i usually win.
I use concusion over flash becuase of preference (anyone wanna debate the two?)
all three of my perks help with being a moving sniper.
The best attribute a sniper can have is being able to predict people. learn routes that people take and be ready for them.
If you want stealth, then you definitely need a silencer. Especially with a gun like the .50 cal. The perks listed earlier are perfect. Also, when it comes to your secondary, don't worry about stealth. Go for a machine pistol. This is to help you make your way to your sniping post. Honestly, I can not quickscope for my life so I need an automatic weapon to get me somewhere.
As far as maps go, I don't feel there are any legit sniping maps in this game. WAW and MWR was loaded with them. Black Ops had Array. But in MW3, there aren't any maps for snipers like myself. I like to get somewhere, throw down a claymore, and look down a long road or something. I have become quite effective when it comes to lead shots so my sniping skills are pretty good. I haven't tried sniping on MW3 yet because there just isn't any good maps to do it on.
When it comes to the sniper itself, bolt action is the way to go. In Black Ops, I always went with the L96A1. I never put a silencer on it because I felt even though the stats didn't show it, the damage was decreased. However, if you're gonna skip out on an automatic secondary, go for the semi-automatic sniper like the .50 cal. This way you can at least attempt to work your way to a good sniping post.
I use ACOG. Most of the maps are too small for me to effectively snipe, even Outpost.
Stealth Sniping class.
AS50 w/ACOG & Silencer
What I would run as a stealth sniper. Marksmen may seem out of place with the ACOG, but the long distance notification is just too useful for a sniper.