If you are going to look after your bike properly you’ll need the proper tools and supplies. Here I will list the more basic necessities for keeping your bike in top riding condition, to do certain jobs you need specialist tools, these are expensive, so its better to take your bike to the local cycle shop and get them to do the more complicated repairs.
These tools you can buy in any hardware store or tool specialist, they can be found anywhere, the more you spend, the better quality tools you’ll get and hopefully they will last longer.
Various size screwdrivers.With these tools you can do most jobs, anything more complicated you are better to get the bike mechanic at the shop to sort out.
On most bikes these days Allen keys fit nearly every bolt or nut, the 5mm Allen key is the one you’ll use the most, the brakes, the seat, the gears and all the bolts on the stem for tightening onto the steering column and all the bolts to clamp onto the handle bars, occasionally the 4mm Allen key is used for the bar clamp and for brake blocks, some V-brakes on mountain bikes need a 2.5mm to adjust the tension on the return springs, the 9mm you need for crank sets and pedals, some pedals need a open ended spanner, but most now use the 9mm Allen key.
You will need a chain link tool to fit a new chain as you usually have to shorten a new chain that’s straight out of the box or if you snap a chain it can be repaired, tire levers are a must for repairing a puncture or fitting new tires and cable cutters and pliers for cutting and crimping cable ends on brake and gear cables. 
As well as tools you also need oil and grease, its best to have a thin spray oil for cables and a heavier chain oil if you live in a wet area, in a dry area you can get away with a lighter chain oil, there are many different kinds of chain oil (some very expensive) ask your local shop as they will have the best knowledge for your area and they will take into consideration if you ride road or off-road.
Grease you need for the gables, hubs, bottom bracket, heat set and any other moving parts. Many headsets, bottom brackets and hubs are sealed units and cant be greased and when they are lose or worn must be thrown away. Grease or oil any parts that move and your bike will work longer and better and with the right tools you can tackle any jobs.
Why rip the crap out of nuts on your bike with an ancient adjustable wrench, a socket set and spanners to suit the nuts on your bike come at a very cheap price no need to strip the sides of your nut with crappy tools