I'm not sure if this is the right place to ask, but here goes:

I'm new to cycling and I'm looking to buy some basic tools to fix my bike in case it breaks down or gets a flat on the road (even if it's just a temporary fix until I manage to get to my bike shop!).

What tools should I be looking for? Are there any basic maintenance kits that could cover my needs?

You could go to your shop and ask them. I'm guessing they'll be very helpful and explain and show you the options.

For break downs on the road if you can handle your own flat tires, you are about 95% covered. I'll carry a folding multi tool or something like that with me until I get a new bike sorted to my satisfaction but I've ridden for years carrying only a spare inner tube and a CO2 inflator.

For maintenance at home it depends on where you draw the line what you're comfortable doing. You'll be surprised at how much you can do with just a 5 mm allen wrench. Beyond that I recommend acquiring tools selectively as you find that you need them. And, when you decide to buy a cable cutter, step up and get a good one. Nothing is more frustrating than a brand new cable cutter that leaves one strand uncut.

I will depart a bit and recommend that your first purchase, after a spare tube and CO2 inflator/pump, be a copy of tech data such as the Park BBB or Zinn's book. I prefer the BBB as it seems to me to be a bit more relevant and clear. While having the right tool for the job is important, having the right knowledge is more so.

For the road:

Spare tubes (presuming you have inner tubes), tire levers, pump. It's unlikely that a properly maintained bike will need anything else other than these. A friend of mine never takes any tools whatsoever and just says repairing at the roadside isn't worth it - unless you're going far out from home. I laugh but I do think he's right. I don't always have someone to call on to pick me up so having a spare tube, some levers and a pump can be a lifesaver.

At home I would get:

Lube/grease, chain oil etc..., plenty of old rags, chain link extractor, screwdrivers (you might only need one type), allen keys (might as well buy a set 4/5mm are most common), pliers, cable cutters, a good adjustable wrench, any relevant 'special tools' to get your crankset, bottom bracket and cassette off (these are dependent on your parts) and some spoke tools.

I second this recommendation. Besides the Park Tool Big Blue Book, I also like Bicycling Magazine's Bicycle Maintenance & Repair book.

I've slowly collected tools over the last almost 30 years. When I was a new rider I wish I had got a basic tool kit like this one right off the bat:

Nashbar Essential Tool Kit

With that kit you can install chains, remove cassettes, fix flats, remove cranks, adjust headsets, have an allen tool for every bolt on your bike, ect... It blows when you need to work on something and you don't have the tool. Then you make an emergency run to the bike shop and buy a tool for triple the price.