Hi Ovidiu
I was in a very similar position to you last year, got my licence in 2007 but still hadn't got a bike. I went looking for a strom with the same £2-3k budget and wanted an ABS model. It took a few weeks of searching and I did start to look at a few bikes above £3000 but eventually I found an '07 Wee with ABS and 11500 miles on the clock advertised on this forum for which I paid £2250, and I'm very, very happy with it. My advice would be to stick to your budget and keep looking. There may not be many private sales around just now as it's the middle of winter but that will change as riding season approaches. Keep in mind that a very shiny looking 2015 Glee with only 4k miles just sold on here for £4550.
Dealers/private - dealers are always going to be more expensive as they have to make their profit. For me it wasn't worth it to pay the extra, not that I didn't consider them, just that I couldn't justify the extra cash for a lesser specced bike. I knew next to nothing about how to go about buying a used bike, in fact I've never even owned a car, but there is some great advice in LaKraven's post in the for sale section that Gassoon linked to, read that and also the guide that I linked in that same topic. That should give you some confidence to go and look at private sale bikes. Obviously, if you have any mates who are into bikes ask them to view some bikes with you.
As for accessories, sure, all the guides seem to suggest they shouldn't factor in the price but try telling that to the sellers! Have a good think about what extras you really want/need. For general bimbling about and a bit of off road a sump guard and crash bars will be more useful than a top box and panniers. The one thing I would suggest will always be useful is a centre stand - just makes maintenance like oiling the chain so much easier. It will work out more expensive to buy and fit things yourself but you don't want to be paying above your budget for a bike with loads of bits fitted to it that you don't care about. How important is it to you to have a fancy after market exhaust? Then again, you could maybe take things off and sell them to make some of your money back?
The Wee has been a fantastic first bike for me. It has enough power that I don't think I'll get bored of it soon, it can still scare me if I ask it to but is very easy to handle and ride sensibly and gives me confidence. For shorter riders the height might be a problem but from what you say it sounds like you'll be fine. I can't speak for off-road use as I never intended to do any, and as my bike came with lower fairings I still don't! I use it for fun riding around the countryside, some commuting and discovered touring when I went for a two week trip last September - all the way to Berlin and back. I really can't fault it as a great all round bike.
Kit and experience to ride it home - when I was looking I had to discount bikes that were a long way away because I didn't want to buy without viewing the bike in person. I still had all the necessary kit from when I did my test years before. Surely you will have to get the kit at some point if you're ever going to ride it? I also went for a "Back to biking" day with a local instructor (on one of their bikes) before I bought mine which gave me a bit of confidence that I could remember how to do it! I was still nervous as I rode my new bike home, especially as I timed it badly and it was rush hour - a journey that I'd now do in less than an hour took me about two, sitting in traffic not wanting to filter. The point is that the experience will only come from riding the bike, you've just got to get on with it! Good luck with everything, you won't regret it