(Core Set Perspective)
Since the card pool in the Core Set is quite small compared to where the game is now, one of the benefits is that you know (roughly) what to expect from each faction. With that in mind, I thought it'd be a nice idea to list some general things to think about, at least for when you're just starting out. As always this is very much my own opinion, so please feel to add to/correct what's here with your own points!
Import some breakers. Using your in-faction fracter feels like trying to pick a lock with a marshmallow. You may also notice that you don't have a decoder, so unless you want to rely on Crypsis you might want to do some shopping around.
Attack the Corp's money. You're a Criminal, it's what you do. They can't keep you out if they can't get their stuff online. You can also make money from their unprotected servers. Compared to the other factions, you've got the highest chance of swimming in cash. Which is good! Because...
You have some of the best evasive tools in the box. Is that an ice you see? No problem. Skip over it, swerve around it, sneak behind it, flip it or kill it; so many choices, and you don't even need a rig up. Very Criminal. Just be wary of hording them because...
Damage hurts you more. Since many of your best abilities are kept in-hand, losing them will cause you more problems, and one of Criminals innate weaknesses is they can't really get stuff back once it's gone.
Your console is amazing, but you only have one. Not sure what the consensus is, but I seriously consider sticking with a crap opening draw if I find this among it. Think of your hand like a party, and Desperado as the cool unassuming buddy who shows up and just makes you happy, even if everything else is terrible.
Lastly (for now at least) you have a lot of nice cards, but you've got some arguable duds in there as well. Lemuria Codecracker encourages some bad crutch-forming habits. Data Dealer is only really worth it against Weyland, sometimes, and both Crash Space and Decoy are components of an at best delicate defense, that (might) protect you (mostly) from something big (once).
Protect HQ. If you've played any of this game at all, you'll already know why.
Most criminal events rely on you not preparing for them, so in most cases if you do things like, double up on ice, keep your best ones in the back, cover your sides and so on, you'll take a lot of the sting out of them.
Kill their stuff. No-one likes it when you kill their stuff, but for Criminal it can be particularly annoying. In general, they can find whatever program they need with pinpoint precision, three times. Beyond that they have to dig, and they're not good at it. A well-timed removal of an important card will probably slow them down, and might even screw them completely. This lead right into...
Packing some traps. As long as there is even the threat of damage you stand to gain from it. Criminal can't recover from a hit to their hand or rig as readily as the others factions, so there's a good chance they will play more cautiously. Ironically, the better the cards they have in hand, the more threatening your nasty surprises can become.
Seriously, protect HQ.