I suppose the nub of the question is what do you want to turn, given your space concerns I suspect that you might be better off with one of the smaller lathes like
this one. That's got enough space over the bed to let you turn something thats around eight inches wide, and enough length to turn a reasonably sized spindle, plus you can get an extension for the bed if you want to turn longer things. Electronic speed control is also quite a bit nicer than the mechanical speed control on the AWVSL1000.
You'll find that if you try to cram the AWVSL1000 into a space only as big as the lathe is, you'll have to slide the headstock up the bed to get proper access to the workpiece, as you need a reasonable amount of space around the toolrest so that you can move yourself and the tool with ease. The further up the bed the headstock comes, the less point there is in buying a big lathe like the 1000.
The tools are certainly good enough for you to make a start with, I've got the skew, spindle gouge and parting tool in that range and they're all perfectly functional and a good jumping in point if you're just looking to get into turning. To be honest if I hadn't been given a bunch of gouges for my birthday I would have just bought that set myself. I've certainly seen fantastic pieces turned with them at both of my local turning clubs, so the tools needn't hold you back.
You'll want to keep hold of the grinder, you'll ruin waterstones sharpening gouges on them and it'll take forever and a day to do so. The objective of sharpening a turning tool is to give it a reasonably sharp edge in as short a time as possible with a consistent bevel. Turning is very different to using hand held chisels, in that the wood is hitting your chisel at anywhere between 20 to 50 miles per hour. This will knock off any sort of carefully ground and honed edge in seconds, so you needn't waste your time sharpening to a razor edge. Use the white wheel and ignore the grey one, and check out
this site for a good sharpening jig setup that's cheap and easy to make.
Speaking to your package, if you got the little lathe I mentioned above (£173) and the set of Axy chisels (£63), that leaves you around £100 left to play with. Other things you'll need are some abrasives,
these to start with and then for finishing
Micromesh is good. You'll also want some sanding sealer (try Chestnut Cellulose Sealer) and some wax (again Chestnut do good stuff, I use their microcrystalline wax). That should leave you somewhere around £50 under budget, which you can go and spend on some nice turning blanks once you've got a feel for it.
