At the risk of sounding boring, I really would suggest getting decent measuring and marking tools. I'm a novice (woodworker, not nun), and found very quickly that there's little point in having good cutting and planing tools, if the stock or workpiece is out of square or smaller/shorter/longer/thinner than you'd intended. It can be absolutely maddening.
Top of the list, I think, would have to be an enginneer's square. Absolutely indispensable: it's the first thing I reach for when in the gar...workshop. It's a real eye-opener if you test a run-of-the-mill so-called carpenter's square against the engineer's variety. I picked up a small incarnation of the latter for about £5.
Second, a marking guage. I like the wheel-type ones, and see that Alf has suggested the Titemark-Lie Nielsen version, which, no doubt, is excellent, but it makes a hefty £67 pound dent in one's wallet. I've got Axminster's version, which isn't too shabby, and comes in at about £17.
Hope the above hasn't given egg-sucking instructions to a gandparent.
You've mentioned chisels. I steered clear of Japanese ones, because some can be very short, which might present sharpening problems. Also, some of them, I believe, need their handles to be finished: something to do with the hoops and belting them with a hammer. (Apologies to the better informed, who are no doubt wincing at my ignorance.) On the plus side, though, the backs of Japanese chisels are easier to flatten, I suspect.
I've got a set of Kirschen/ Two Cherries chisels, and I like them. Their edges last quite a time (although nowhere near the time of Jap. chisels, I imagine), and they feel good in the hand, although Alf, I seem to remember, doesn't like the varnish on them or the hoops, which she thinks look cheap. On the down side, whilst the Two Cherries come mirror-polished, I found that that doesn't mean the backs are flat; I took a great deal of time flattening them on waterstones. Yet, on balance, I think these chisels are a good buy, and you'd have to pay a lot more for anything significantly better.
As for saws, you might want to keep an eye on ebay or at boot fairs for good, old saws. I have a couple of Disstons that are wonderful. However, if I had the pennies I'd plump for the Adria or Lie-Nielsens. One note of caution, though, on buying a decent saw: unless you want to learn how to sharpen a back saw, you need to find a good saw doctor, who won't just use a machine to cut new teeth. Someone on the forum even encountered a saw doctor who didn't know the difference between a rip and x-cut. Not good if you send or take a £100 saw to a nit-wit. For what it's worth, a while ago, I posted an address for Davenport Saws, who might be good; I seem to remember that David Charlesworth, a hand tool guru, also recommended them.
You wrote that you were wary of using a powered sharpener, given the risk of overheating the steel of the tool. I agree that the run-of the-mill bench grinders can be a nightmare: I've inadvertently turned cheap, normal length chisels into butt chisels that way, and wouldn't let my Kirschen chisels within 20 feet of my grnder. There is, however, a well-known wet grinder that is highly regarded by some: the Tormek. Yet, at nearly £300 pounds, its purchase might be grounds for divorce, unless, through guile and Special Forces tactics, you manage to sneak it past S.W.M.B.O. I've recently been using watersones, but find the constant need to flatten them a pain in the rear; they can also make a ruddy mess, and I remain concerned that getting water near anyting made of steel is asking for trouble, although I have recently seen an advert for some potion or other that can be added to the water to prevent rust.
You might want to try something called Scary Sharp (google it), which is a sharpening technique that uses a succession of different wet 'n' dry grits to flatten the back of, and sharpen, plane and chisel blades. I liked it, and it taught me a lot about sharpening, but you may find you don't like the messy spray-glue or running out of sandpaper when you most need to sharpen something. I think I actually prefer it to waterstones, which I am beginning to dislike.
Apart from the above, planes, planes, planes. But be careful, they are addictive. Completely, utterly, absol......
Well, I hope some of this is useful, and that you'll forgive me for waffling on.
Js
