Getting started; beware!

I you never have had a garden model railway it is wise to consider some things before you get started (or shortly after):

- Time
- Money
- Operation

Time 

Plants taking over
(picture from my old railway)

Time is for some a fire in which they burn and for others an ocean to swim in.
If you would like to start a garden railway and you don't have much time to spend on it; keep it small and simple!
Only if you have plenty of time you can consider a bigger garden railway. Garden railways can be very time consuming. Other than indoor railway layouts the maintenance of an outdoor layout is significant. Leaves and branches on the tracks, garden plants taking over, turnouts that need to be clean, little critters attacking your buildings, rain showers that cause floods and winter frost heeves that can cause damage. Do not under estimate this. The bigger the railway, the more work there is!
Keeping a railway small and operations simple can reduce maintenance and time.

Money

Garden railways don't have to be expensive! True; if you like a full scale Orient Express with live steam engine and 12 coaches running through a large layout you will have to able to spend a lot of money. But I have seen beautiful layouts that vary between dirt-sheep ones and some unbelievable expensive. You CAN build a nice layout on a small budget for sure!
I think you have to find a balance between what you can (or want) to spend, what you like and again; the time you can spend!
For instance; personally I don't like the main stream and 'out of the box' trains so I am not tempted very easily to buy expensive models. I am a little bit handy and love to use my imagination so I bash or scratchbuild my models that are often based on secondhand stock bought from auction sites. With some skills you can make your own, unique, models and safe some serious money. Than again; building these models take more time than buying one. Balance is everything...

Operation

There are some main types of operation; track powered, battery powered, clockwork and live steam.

The most conventional is track powered; the trains run by electricity through the tracks like most model railways. This way it is also possible now-days to digital control your railway by using decoders and stuff. The downside in my humble opinion (based on years of experience on my old railway) is that track power ALWAYS cause problems. Even the best perfect laid track eventually will show problems due to the fact the track is outside and under influences of moisture, temperature changes and dust. You have to maintain and clean the tracks almost constantly to ensure some smooth running but often you will face problems. This is actually one of the biggest frustrations of garden model railways.

The railbus is battery powered. RC controls came
from a cheap RC car toy.

This made me converse to battery powered trains. They will run undisturbed by dirty tracks and run smoothly even over not so perfectly laid tracks as well. Battery powered trains are often operated by radio control (RC), meaning that you have to build in a speed controller and receiver and you need a radio controller to operate the trains. In the past RC control was not a great solution because of interference disturbing the signal but since the 3,2 Ghz are on the market (for affordable prices) this problem is no longer an issue.

You can use common RC equipment you can buy in any hobby store (local or online). You can also experiment with (cheap) RC electronics that are used in remote controlled toys, like cars and boats. However these can cause interference problems and have a limited range. They will work well as long as you keep close to them. 
There are some companies that produce RC equipment especially for model railways as well. Off course you can also run battery powered trains without a RC unit; just letting it run its rounds. If you just enjoy seeing the train running through the garden this is actually a good option.

The oldest types are off course live steam and clockwork.  

Clockwork is not very common and only some collectors run old clockwork trains on their layout. Actually I only mention this type of operation te be complete ;-)

Live steam is a very beautiful way to operate the trains as the engines are powered by hot air like real steam engines. Most of these models now-days are gas fired engines. The trains are mostly RC controlled. However, this way of operation request some more work than the other types. It is not just place it on the tracks and play! You will have to fire up the steam engine for instance and you will have learn how to operate these trains. Also they need some more maintenance and care. Live steam models are by rule always expensive.