Just to go Nerdy for a moment (sic) and consider the insides of the camera ranges.
A compact camera has a very small sensor in it (the thing were the light reaches to record the image it sees). An entry level dSLR has a much larger sensor (and full frame one has a very large one).
The difference between compact and dSLR sensors govern the quality of the photo, especially at larger sizes (in particular for printing).
If you are hoping to print off some larger photos then the compact will give much poorer ones because the small sensor is not as capable of retaining and reproducing detail. However if you are likely to only ever get the photos printed at 6x4, 7x5, or maybe 9x6 sizes from Boots or Jessops, then a compact will in most instances be fine.
If however, you fancy putting your masterpieces on the wall, then dSLR (even entry level ones) will allow you to print A3 or even bigger and will also let you get made some rather large canvas prints too.
A compact has it lens built in and the lens is maybe going to be a large as a 2p coin at its widest aperture (aperture is the part that opens up to let light into the camera).
A dSLR lens will be far far larger and this bigger glass element will also be a higher quality in most instances. This larger lens combined with the larger sensor is what gives you more quality combined.
That said, an expensive compact will give you very good results, but it limits your creativity, using in-built creative modes to let the camera do what it thinks is right, whereas with a dSLR and a range of lenses means that you can be in full control of what you want to get out of your photography.
Don't get fooled by 60x zoom on a compact - when a small lens does that, it will perform less well than you would expect.
If you want a second hand dSLR and lens, look here:
https://www.mpb.com/en-uk/used-equipment/used-photo-and-video/used-digital-slr-cameras/
https://www.mpb.com/en-uk/used-equipment/used-photo-and-video/used-lenses/
Bilbo.