I second Janome as a brand having just invested one myself. The one I got is slightly out of your budget but you could probaly find a second hand one on ebay (or even on here!). Like KVT, I think they make the John Lewis own-brand machines too.
The John Lewis website has a guide to buying sewing machines on it and the sewing machine listings can be filtered according to budget and level of skill, so it might be worth having a look on there. I found it very useful.
Another option may be to hire one to try it out? This site has a list of places which hire out sewing machines, although I don't know how up to date the list is:
Regarding accessories, most machines will come with everything you need for basic sewing but as KVT said you may need to buy a few extra bobbins and a zipper foot, depending on what you are planning on sewing.
Hope this helps.