The maintenance you need to do depends on how many miles you put on the bike before it went into storage. Assuming you were riding it regularly between 2011 and it going into storage you just need to do a 'well used bike refresh' which includes replacing a number of parts that wear out.
As others have said, start out by giving that poor bike a good cleaning. It was not a good idea to store it wet and dirty and that may have contributed to some of the problems you are seeing now. As part of that process thoroughly de-grease the chain, cassette, rings and rear derailleur idler wheels. There are a number of bike cleaning videos out there that make recommendations for cleaning supplies.
You will need a basic tool kit: hex wrenches 2-12mm, open-end/box wrenches 6-17mm, small and medium needle-nose pliers, set small to medium flat and Philips screwdrivers. On some bikes with disc brakes a T25 torx wrench is needed. A bike-specific torque wrench is nice to have. I'd recommend at least a 2-8Nm one for small bolts. You'll have to decide if you want a larger one (up to about 15Nm) as well.
There are many good instructional videos available on all aspects of repair and maintenance. I personally like Park Tool Company's YouTube channel. These will tell you the specialized tools you need, but I'll mention them below as well.
Go over the bike and check for general obvious problems and loose bolts or fasteners.
If you were riding the bike regularly a new chain is a certainty. You will also need to check the cassette sprockets to see of any of them are too worn, and replace the cassette if required. If you need to replace the cassette you will need a chain whip and cassette lock-ring removal tool. I believe most lock-ring tools require a 25mm wrench, a large adjustable wrench will work. You may want to invest in a chain wear tool as well. Chain rings wear more slowly than cassette sprockets but check those for excessive wear also.
While you have the chain off, check the derailleur idler wheels, if they do not turn freely they will need servicing and re-lubricating, or just replace them.
Also with the chain off, check the crank spins freely in the bottom bracket bearings. If it does not turn freely, but there is no roughness you may be able to service the bearings. Research the particular type of bottom bracket you have for serviceability. If there is resistance and roughness it will need to be replaced. You will need the appropriate external bearing bottom bracket removal tool for your bottom bracket.
I don't know if chain quick links existed in 2011. If yours does not have one you will need a chain tool to break the chain, and to connect the new chain if you get one without a quick link.
When the new chain (and if needed, cassette and rings), perform a full front and rear derailleur adjustment (Park Tool's derailleur videos are particularly comprehensive). It's more than likely that you will need to replace the derailleur cables and housing to get your shifting working correctly. It's a good idea to replace them anyway. You'll need a special cable and housing cutter.
Service and adjust the brakes. I'm guessing they are mechanical disc which I don't think require special tools (someone please correct me in a comment if I'm wrong here). As with the derailleur cables the brake cables may need replacing. The same housing and cable cutter required.
Check for play or roughness in the headset bearings. If there is play but no roughness you can adjust the bearing tension. If there is a gritty feel you will need to disassemble, clean and repack the bearings.
Check for play or roughness in the pedal bearings. Depending on what pedals you have there may be as service kit or replacement bearings available if the bearings are worn out.
Check the wheel axles for play or roughness in the bearings. Depending on the hubs the bearings may be serviceable or replaceable. You'll have to research your particular hubs. Check rims for trueness and check for loose spokes. If the wheels needs truing I recommend having a bike repair shop do it.
Forks and rear shock may need re-build or servicing but that is beyond my knowledge.
The various creaks you will have to individually hunt down and address.