There are many conflicting views on this, but for what it's worth, I would never, ever buy part-worn tyres - having spun off the M1 motorway many years ago, my father and I learned a very valuable lesson in tyre purchase - which was reinforced by a mechanic friend of mine I met since then who has one firm piece of advice - 'if nothing else, buy the best quality tyres you can afford as these are the things you reply on to stop and which may prevent you from having a very serious accident.'
Also - tyres do have a lifespan (rubber degrades over time even if unused) of somewhere between 6 and 10 years (you can find out the date of manufacture from the DOT reference on the side of the tyre). Unless I had no other option, I would never purchase a tyre that I intended to use immediately if it was more than 6 years old (and for all normal purchases, I would only purchase a tyre that has been manufactured in the last 12/18 months).
In recent years, the best performing and most durable brand I have used is Michelin - I had a set of Michelin Primacy tyres on my old Mini Cooper which lasted 25,000 miles - the extra cost was wholly worth it and proved to be considerably more economical than the cheaper tyres I have purchased in the past. When my current Michelin Energy Saver tyres wear out (just purchased a Honda Jazz 69 plate so they have very little wear), I'm going to fit Michelin CrossClimate tyres - there are a lot of excellent reviews about these online.
One final thing - in recent years I've started to purchase tyres online through BlackCircles (after having researched a lot of similar retailers) - and have made significant savings - you buy online and book into a local garage - never had any problems and would thoroughly recommend them.