If you want to have a reasonable life out of them (long term use) Make sure they are HSS and from a quality supplier.
Cheap sets are likely to be Carbon Steel, often quite good and sharp on the clean cutting front and ideal for thread clean-up and the occasional use in softer materials, but be prepared for loosing their cutting performance if used regularly and Breaking if not used with care.
A lot of folks start by purchasing a Carbon steel kit in a reasonable case(steel) and replace often used pieces with higher quality HSS as and when they loose performance or break.
Broken Dies are no problem, they just fall apart, a Broken tap is a far more serous problem as they invariably are impossible to remove as they break because the are jammed tight in the hole being tapped.
It is not impossible to Break a HSS Tap, but you are really into the 'used without due care and attention' world if you do with a reasonable quality brand.
What is often forgotten is a set of CORRECT sized Tapping Drills to go with the taps, for some obscure reason it is rare to find them supplied with the taps in sets.
Tapping kits often have only two taps of each size Taper and Finish.
Better for blind holes and less risk of breaking one, is a set of three taps in each size, Taper, Intermediate and Finish.
It depends on how serious you are Mike, what you want to do with them in what materials and how often.
I absolutely agree that if possible buy decent HSS taps but if your projects are mainly for just a few sizes I wouldn't buy a set as the majority will remain unused, better imo to just buy what you want but better quality.
Good ones aren't cheap but Chronos might be worth a look and if you watch fleabay carefully yo can often pick up quality industrial job lots.
That said, I have a set that's now at least 30 years old and a mixed collection of others I've picked up over the years, bought a few more at Harrogate show in November. The ones I use regularly are 4, 5, 6, 8 and 10mm but there are occasions I need to match a thread.
My metalwork is just odd projects and repairs / modifications so a very light user.
Just to add to Chas' excellent reply [Edit - and the others while I was typing], a Zeus book will help with finding the correct drilling size and you might also see Intermediate taps referred to as Second taps.
Also a tin of cutting compound will make your life a lot easier. One tin will last a woodworker for life.
The only thing to add to what has been said before is that HSS taps of the smaller size will break in a heart beat with any lateral force or if they are not frequently withdrawn and cleaned of swarf.
I’d only ever buy eactly what you you need, 4mm to 10mm are usually the predominantlay used. I’d recommend Dorma (expensive) for production use or Presto for home use. The best quality tap and die holders are also extremely beneficial.
As an aside, I made some jigs recently and tapped holes in wood using a cheapo set of taps and these worked fine. It seems to me that when you have taps & dies you find uses for them you didn't initially plan.
I buy what I need, though I did purchase a very inexpensive set of spiral taps from China just to test them out. M3-M12 less than £10 for the set. They are my new favourite taps, superb quality, sharp and work great. They might not have the DIN spec for industry but for the home shop they are incredible value.
Unless you are doing something odd like making small steam engines, you'll find you only need a very few sizes anyway. I bought only as/when I needed, and better quality sets of three taps at a time. I think the Chinese manufacturers often throw in sizes like M7 because they make the set look good, but you'll probably never ever use them as they're non standard. And one really useful one you never get in a set is M3.5 for electrical boxes...*
One trick I've seen toolmakers do is to grind off the nose of the third (bottoming) tap, to get it to cut further down into a blind hole. I've got a couple of mine like that. Obviously you can change the hardness if you're not careful to keep it cool when grinding.
Only the far end of the tap actually does any cutting (the tapered bit). The rest of it supports and drives the cutting end and probably polishes the cut thread a bit. So if you are looking at taps to buy, see what the tapered part looks like - if there are chips to the cutting edges or they're not well shaped, avoid.
If you go down the "assemble a kit myself" route, it's worth having a couple of different types of tap holders. I've got both the long handle and tommy-bar types, as they are convenient in different situations. It's also much nicer to use the pillar drill when practical - chuck the tap, remove the belts and use the pulley as a handwheel. It keeps the alignment spot on so you get a nicer thread. I've occasionally hung a weight off one of the quill advance handles, to defeat the spring and maintain a downward pressure. Putting a slight countersink on the hole also helps the tap start.
... really old boxes are 4BA, which is annoyingly close to M3.5. Both threads will jam if you try to use the wrong mating thread, and you can't usually re-tap any 4BA hole to M3.5 as there's not enough meat left. You can get M3.5 taps with a glued-on handle though, for cleaning threads.
Very useful stuff, folks. Thanks very much. I shall digest, and then start looking around at what is out there. Mine would only be for very occasional use, but I've got a router-plane build in mind at the moment, and I want a screw depth setting arrangement. Either a tap or a die, depending on the design, is likely to be necessary.
I like Tilgear - have bought from them in the past and been pleased.
Brass takes threads really nicely and easily. If that's all you want it for, an inexpensive set should be fine. Stainless and cast iron, however, can be rather awkward, especially when hand tapping.
I've done the latter a few times (repairing old fireplaces), and it's not awfully nice. Would politely suggest a bit of practice beforehand in that event, and using the best quality taps you can find easily. It's the crunchy feeling that tends to be qite offputting...
Lots of good advice there. Just a couple of points:
1. When getting taps it is really useful to get so-called 'progressive' or 'graduated' sets. The starter tap is not only more tapered at the start but is a thinner diameter, and they progress as you get to the final size. Sometimes hard to determine from an advert. The set below is graduated and was cheap on eBay though there is no indication on the box!
2. Brass is very easy to tap or thread, aluminium is harder (lubricate with WD40) steel and cast iron are not too bad (use cutting fluid), stainless steel is terrible (cutting fluid and good quality sets). For a nice looking and smooth plane adjuster I suggest getting a bronze rod (bit stronger than brass, but that would be second best.
3. When tapping, get used to taking a half-turn cut, then backing off the tap till you feel the back of the flutes on the tap cutting off the scarf (hard to describe, easy to feel). Otherwise it will clog up and jam, and ruin the thread.
4. When die cutting (much harder to get a uniform thread rather than a drunkard's walk) make sure you have a good tapered lead-in to the thread. Don't rely on the taper of the die itself. You can always start with a longer piece and cut off the taper afterwards.
5. Where possible use a machine of some sort to keep it all square, especially when starting and especially with a die. A lathe with dedicated tap/die holder is ideal, but drills and even a vice can be used if you have to.
Note that I am Welsh, and a couple can be anything up to 50 ;-).