First service, lubrication, multi tools, degreaser, inner tubes, pumps and bike covers
Okay, so you buy a bicycle and maintenance is the last thing on your mind but it's good to start as you mean to go on.
I know that it sounds strange but once you take delivery of your new bicycle, book your first service. Most bike shops give you a complimentary First Service a few weeks after you buy a bike from their shop so make sure you get them to check that everything is working well. They will set the brakes, adjust the gears and do a few checks. Make sure that you insist on this service (they won't necessarily tell you about it until prompted).
The first thing that you have to do is tell them not to go anywhere near your bike with that horrible, cheap, black grease. If they do (as they did to my bike), any trousers you wear on your bike will be ruined. End of. All the degreaser in the world won't remove it completely. Instead, get yourself a bottle of White Lightning Clean Ride self-cleaning wax lube. Now I'm not a shareholder (I promise) but this stuff is fab. Shake the bottle, apply liberally to everything that moves (chain, pedals etc) but not anywhere near the brakes and let it dry. The idea is that the wax lubricates your bike but flakes off gradually and the dirt flakes off with the wax so you don't have to degrease and clean between applications. If it rains, lubricate more regularly. It really is that simple.
Degreaser isn't completely useless. There is so much grease on the road these days and it's a pain to remove it from your bike with liquid soap on its own. You might want to get some degreaser for bicycles and put that in amongst the suds to really remove that grey, clumpy dirt that is born of oil and dust.
Get yourself a multitool for bicycles like this one. It has the universal allen key that fit most of the adjustable parts of your bike so if your seat suddenly shifts or your brakes slip, you can help yourself on the side of the road - or get some good Samaritan to do it for you if they stop and offer to give you a hand.
One other thing that you just have to have with you at all times is a spare inner tube and a bicycle pump. If you don't want the spare inner tube to take up space in your bag, get a saddle bag and stuff it in there with the multi tool while you ride. You can fix the pump to your bicycle frame so that's no biggie either and the multi tool has those "spoon-like attachments" that enable you to change a tyre. Find out how to do this ASAP! One quick note on pumps - don't buy one that is too small. The smaller they are, the harder you work. Get a basic one about a foot long with interchangeable heads and it will do the job without costing you too much money - or effort.
I have tried keeping my bike covered with a PVC cover but the birds ruined it, it got dirty and the bike still rusted a bit underneath. The jury really is out on whether or not you should cover your bike as some say that condensation still forms under the cover, causing your bike to rust that bit more. So I don't bother anymore and all is still well in my world.