My favorite combo so for has been the Mastermind-Enforcer.
I've been toying with the build calculator.
http://www.pd2skills.info/This is also Overkill Approved. It's good and has a slider so you can set your level which helps when you are as bad at falling into trap skills.
I had that Enforcer skill for infinite ammo aced for a long time till I realized it makes you put your ammo bag in AWFUL places and you still have to reload if you come to the end of your magazine so 3 of your 10 seconds on free ammo are wasted.
But yeah Shadow Raid is infuriating. I've done it twice, and both times it took at least 10 tries and over 3/4 of those were due to random guards being able to see me through walls or noticing a bag of loot that was in the sewers even though they weren't near it.
Did Framing Frame on Hard full stealth once.
It was tough and to a certain degree highly frustrating due to there being to many guards not enough pagers but we got it down.
Also back to build information regardless of your core class, I have some abilities I consider required for anyone who is still leveling up. 7 points in Mastermind Unlock, Aced Cable Guy, Basic Fast Learner and Endurance. (Can can drop Fast Learner once you cap levels.)
5 points in enforcer. Unlock and Aced Transporter.
11-14 Points in ghost. Unlock, Basic Cat burglar, Aced Fast Hands, and Shinobi at least basic but can be really nice to have it Aced for certain situations.
Unfortunately this does seem to preclude you from getting top tier rewards from two classes though.
EDIT: Also Cable Guy is completely optional if you already have more than 10 million in spendable cash on hand, since you can just execute all the hostages if you don't care about money.