I am needing a new camera. I would like a DSLR type one, because I played with one, and I liked how quickly it captures the photos and the quality.
Im not a photographer, but I want to use it to capture family moments. Im not bothered by second hand stuff either.
Any recommendations on what I should be looking out for, my budget is a cheap as possible without not being worth it

If 'all' you want is a camera that takes photos quickly and at a good quality then you don't really need a DSLR, you may well find that a 'Bridge' camera (a camera that's half way between a Compact and a DSLR) is ideal. It all depends on what you are willing to accept, how much you want to spend, and how simple you want things to be.
Advantages of a DSLRInstant power up
Takes photos very quickly
Good quality photos at higher ISO's due to larger sensor size
Ability to change lenses
Disadvantages of a DSLRBigger and heavier than a compact or bridge
Ability to change lenses means that you will often lug around two or more lenses rather than one
Dust Bunnies. Each time you change lenses you can get dust inside which appears as black smudges in the photos so you have to clean your sensor.
Potentially more expensive
You can't just sling it in your pocket
Advantages of a Bridge CameraDead Simple to use
Compact, small and lightweight
Powerful zooms beyond which you can achieve with a lens for a DSLR
Cheaper than a DSLR
Most of the features of a DSLR without the price and weight
Disadvantages of a Bridge CameraSlightly slower start up time
Slightly slower at taking photos but only in certain situations (this can be further reduced by knowing how to use the camera better)
You can't change lenses
Image quality isn't as good as a DSLR with a good lens (£200+) but comparable in many situations to a DSLR with an average lens (£80-£190)
If you want a DSLR than as Mr. Lampkins says, take a look at the thread he linked to as it all still applies.
If however you want to look into Bridge Cameras then take a look at the ones from Fuji which I think are some of the best in terms of performance and features for the price. Take a look at the
Fuji FinePix HS20 EXR which you can get for £269