I may well be corrected here, but nearly three decades of mostly used bikes and one thing shines through: the previous owner (s).
I strongly recommend that the bike you buy, should you be in a position to assess it and by your own self confessed lack of workshop experience, be serviced well.
This means that it shifts well.
The brakes work with no squeaking (it itself not overly bad, but the fact they do squeak usually shows the owner doesn't know how to toe in cants/Vs which indicates lack of knowledge elsewhere).
There is no play in the head.
Take the wheels out - there should be a tiny amount of play in the axle in out whilst not compressed via the Quick release and I mean tiny as in you should just be able to feel it. No play can be acceptable if it turns freely when you spin the wheel - and feel for any 'grumble' which indicates pitted bearings.At the same time see if the wheels are true. a little bit out is fine - that can be trued fairly easily.
Check for play in the crank, make sure it doesn't move up/down. It could still have a bottom bracket on the way out but you won't really tell that without removing the crank, but they are considered a consumable these days.
Ensure you can slide the seatpost up and down - take it out and shine a light down the seat tube to show up any corrosion if it is a steel frame.
The general condition should look like someone cared for it. If in doubt, just say no. There are a *lot* of good used mountain bikes out there and you will find one that suits for your budget.
This is by no means definitive and I may have missed some aspects but it gives you an idea. If you are buying via post I think that you could do worse than get something from Retrobike classifieds. There are a lot of good mechanics on here and you can see some of them have feedback. Use that as a guide. There may be the odd thing that may need tuning, especially after posting and having to partially assemble, but you *need* to learn some basic craft. It isn't rocket science and mostly it is down to having tools and patience. If something doesn't feel quite right, then it probably isn't. Worth getting something like 'Zinn and the art of mountain bike maintenance'. The stuff is available everywhere on the net, but a book tends to be easier when you are working on it and things don't go to plan.
There is nothing, NOTHING, so satisfying as being able to strip down and rebuild your bike and ride it knowing that everything is spot on. Except maybe building your own frame too.
As for good bikes, that is rather a massive long list. First off, get an idea of what size fits. I tend to know that an 18" is about right for me on a standard 26" mtb. I can tune reach with a stem. Don't get too hung up about the group, a STX groupset with little wear and serviced well will be infinitely preferable to an XT groupset that has knackered chainrings and cassette.
Kona has been mentioned before and they are a nice safe bet as they didn't really make a bad bike that I know about. There has been some cracking GT machines for sale recently for reasonable money that seem to be in very good condition.
I hope this is of some use.
edit - Forgot to say - your Dawes seems like a classic Retrobike project. It is well worth learning your mechanical skills on that and RBer will certainly help you with any questions you may have. Your LBS may be not the ideal place for your requirements, but they can still be used to loosen/replace the Bottom bracket, loosen tighten cassette should you lack certain tools. But get the tools. Get some grease and rags and get dirty.
