I've had a small Chinese elm for almost a year now, because it's my first ever tree, it went through a phase where leaves fell off and it was generally looking a bit sparse- so I let it grow and left it alone for a while. I think I've started to get the hang of looking after it now (it's covered in lovely, healthy green leaves) and I'm interested in shaping and pruning it. I've provided pictures of how it looks at the moment (sorry for the background mess) the tree is neat and tidy, but not a particular style.

If anyone would like to give suggestions with ideas what I can do with this tree and how to go about it that would be really helpful. I'm looking for style ideas and what I can do to achieve them.

Thank you.

The actual style has really been chosen for you already. The style you have is Neagari or exposed roots. It can have 2 styles (like Neagari Cascade) but that will depend on you. I wouldn't worry about style as a style is more of a classification and not something you select and follow.
For styling the elm you need pruning shears and wire to start. I would suggest looking at other Neagari Chinese Elm bonsai for inspiration. If you could find a bonsai club near you that would be even more beneficial. A lot of clubs have helpful members and being around others that have already walked the path that you are on is comforting.
I refrain from telling you more due to not having the tree in front of me and wanting you to make this tree your own.