So from a character-creation RPG perspective (classes, traits, weapon choices and combat styles, etc), how does it compare to a game like Skyrim? Obviously I don't plan to be a wizard, but does allow players to choose between stealth and brute force, and / or ranged weapons (sniper) vs hand-to-hand?
Yes. Well, you'll need to substitute "netrunner" for "wizard", and hand-to-hand gets a new meaning if your hands can sprout a grenade launcher or a couple of sharp blades. But otherwise, yes. Usual system - you collect XP for completed tasks, these translate into level increase, which gets you points to spend on the usual character attributes.
One of the last (well, it's been what, half a year? a year?) updates also added a cloak of invisibility. You'll need a decent level and spend your points on the right attributes, but that can get you up to xx seconds of invisibility. Other stealth attributes will make it harder for enemies to spot you, or easier for you to get out once they've spotted you. You can't always count on those high level specializations in boss fights, however. There is (for example) one quickhack (spell) that prompts your target to suicide. Most (if not all) bosses are immune to that, others will require more than one puny bullet to the brain.
For most of the quests, you'll also have different options of proceeding, depending on your specialization. If (for example) you got the electric shock immunity, you can simply ignore the electric traps and just waltz right down the middle. Otherwise, you'll either need to find a way to switch off the power or find the hidden crawlspace that circumvents those traps (but offers others).
Can you also just go around and fight bad guy gangs, sell loot, and live your own life
Sure. There's just not much to be made from selling loot - main quest episodes and all the side quests pay a lot better (in both cash and XP). Once I got a reasonable level, I usually break down any loot for crafting parts. And the map (for me) is too small to really use this as exclusive playstyle. But there also are a lot of high level items (weapons, clothing/armor, quickhacks/spells) scattered around the map (some of them only appearing when you have a minimum level) which you won't find if you simply follow the main quest.
And you don't need to limit your fighting to the "bad guys" - in a gang dominated city, that's a pure question of perspective. Just because they're wearing uniforms doesn't mean that they're the good guys.
What I don't like about that independent living is that the vehicles you steal can/will disappear if you're not looking. So you can steal (almost - police cars are a bit problematic) any motorbike or car, but you can't sell them - and if you leave them out of your sight for too long (e.g. because you're fighting with the next gang), they dissappear. Vehicles you own (buying, quest rewards) remain and can be called to your position remotely.
Otherwise - sure. Walk around the city, see a gang holding up a kiosk, kill that gang with as much or little collateral damage as you like, grab anything that's not nailed down, take one of their rides to the nearest fence (or automated drop point), cash in. If you're seen killing civilians, you'll get the fuzz going after you for a while. Try not to kill (run over) too many civilians while runnig from them, and they'll give up after a while.