It depends:
(if you don't know) there's single malt and blended. Single malts mean that all the different types of whisky that are blended into a bottle come from 1 factory, blended means more than one.
If you want to drink a whisky with a mixer then try Jamesons, smooth and slightly sweet with no peat or perfume. If you do like a perfumy whisky (ew) then look at bells.
To drink neat:
Have a look at Japanese, due to the distance it needs to travel they only really send good stuff. Yamazaki 10 Year Old again is a very smooth whisky and not expensive at all (£27-30).
My personal preference is Glenrothes or Glenmorange signet. The Genrothes is distilled in an abnormally tall still, giving it a really light drink. The Signet however is on another level! It's honestly like drinking alcoholic chocolate! I could honestly sip it all day
However it's pricey (around £100 when I bought it, it's probably around £130 now).
If you want something more esoteric look at Aberfeldy and Middleton, although they're both not that cheap either. I hate pete- whiskies so I can't really help you there laphroaig is popular though.
As you can imagine, my dad's a big collector of whisky. The best stuff of his that I've tried is the standard Johnny Walker blue. He has the Johnny walker blue King George V too, but he won't open that
Edit: All Londoners should go to The Whisky Exchange in London Bridge. They seriously know their stuff! Very helpful and will allow you to try (in addition to tasting courses) and they're pretty good on price:
http://www.thewhiskyexchange.com/