Buying a second hand decent machine might be a good idea. I have now bought three second hand and each one I sold to upgrade was sold for as much as I paid (in face a small profit). I also bought an expensive grinder. I currently have an Expobar Lever Dual Boiler machine and a Macap M4D Grinder so some serious kit but the coffee is amazing.
As a start I would recommend a Rancilio Silvia machine and probably a Rancilio Rocky grinder or similar. Basically you need a conical burr grinder. The only trouble is they’re not cheap as there is a lot of demand on the second hand market. My first proper machine was an Expobar Office Control I picked up on ebay for just under your budget which was a really good heat exchanger machine and better than the Rancilio I would say.
There’s loads of information on the coffeegeek website including easy to follow guides on how to make a proper espresso and how to froth milk properly. I’d suggest reading around a bit before making a decision.
And for coffee I can wholeheartedly recommend hasbean.co.uk They roast the beans after you order then supply them whole or ground how you want, so are really fresh and the service is fantastic.
Once you get the hang of it you won’t want to drink coffee at most coffee shop chains again as your own efforts should be much better.
I’ve spent a lot but I used to have one or two at Neros or Pret a day so the kit has paid for itself over the last few years.