A lot of other good advice, so I'll try not to repeat anything.
Don't worry about The Grind - you might enjoy it, or you might not, but for starters just try a little trading, exploration, and combat, and see what you simply enjoy doing. Don't get tunnel vision regarding roles/builds - change things up or swap a given module out to try a different piece of gear, even just to see how it works for you.
Also, it's a small thing but unless you're exploring, go into the left panels (X+d-pad left), and on the first tab (Navigation),
use Set Filters to perhaps leave only Systems and Stations visible, also Signal Sources (which show up the Resource Extraction Sites/RES's and combat zones) if you're intending to dabble in
low-level kill stealing combat. Firstly, it's more efficient; you don't need all those planets and stars listed if you don't need that information. And secondly, if you're ambushed/interdicted or need to flee combat, the Systems'n'Stations filter will make it far easier to quickly select a System to jump away (high-wake is a jump, frame-shift speed is a low-wake) if necessary, as some systems may have a list of thirty or forty objects to scroll down or up.
Keep the fundamentals in mind: d-pad left, up, and right shunts power to ship Systems, Engines, and Weapons respectively. If you're in combat and not in a good position (i.e. you're suddenly being shot to hell... ), boost the shields by adding pips. Shunting power to Engines will raise your available speed, thrust, and boosts (B button). If you've got a target in your sights, putting pips into Weapons will allow your energy weapons to fire for longer before they need to cooldown/recharge.
Don't leave the capacitors in set positions and forget about them for the duration of combat or any other activity - get used to changing them to suit precisely what you need at that point (whilst maneuvering). Want to close in on an enemy or just speed up a final approach to a station? Shunt to Engines, throttle up, and boost. Need to finish off a target? Shunt to Weapons and keep firing. Forgot to drop your landing gear and are speeding towards an impact in a station or outpost?! Shunt to Shields! A side-effect of that is obviously that it lowers your available speed, so making mistakes less likely or costly (I think most pad users on Elite have tried to drop landing gear and accidentally boosted to bounce around a station... ).
Oh, and dive in to all the shift inputs, i.e.
hold each face button on the pad to see what all the shortcuts are - from immediately opening the Galaxy or System map, to cycling through targets without having to use free-look, etc. One small example is that if you've set a system to jump to, but for some reason first want to go to supercruise. Instead of going into a panel or hitting Y which will initiate the jump, hold Y and either down or up to enter supercruise without jumping.
(apologies if any of this is patronisingly obvious, or is already second nature)
And lastly; the Adder's a remarkable little multi-role ship that can dabble in all roles. It's very cheap, nimble, and I'd say the only real downside is a fairly restrictive cockpit view given all new players become familiar with the Sidewinder's more expansive vista.
/edit
Keep your sidewinder for as long as you can. Learn to fly in it, fight in etc as if and when you get blown up the replacement is free. / Only once you start upgrading your ship, your modules, and your weapons will you need to start paying insurance.
Yeah, that's a good point, actually. Although a lot of the fun comes from buying new ships and upgrading - early ships have very low buy-backs.