Stick with the main name brands...
I've dealt with numerous electronical items over the years, returned some items that didn't work, or repaired them and I've found normally if you go for proper name brands usually their customer service is ok.
As you will probably find from some of the replies on here or reviews on the internet of different firms, all companies at some point have had some kind of bad customer experience where they've just got it wrong.
This could be due to any number of reasons such as untrained employees or certain shops not withholding the company standards, etc. But normally if you pick a decent named brand even if the shop can't help you, you usually will find that somewhere along the line there is a dedicated customer line that will be able to help.
Brands which I've found to be acceptable in the past in no particular order include - HP, Compaq, Dell, Gateway, Sony, Panasonic, Philips, Toshiba, Fujitsu, IBM, Apple, Acer, 3XS (Scan computers), Alienware.
The only brands I would tend to stay clear of are shops "own brands". Many of the big name brands above have been making computers and laptops for years and have a dedicated team there to help with any problems, but the majority of shop own brands are all made in the same factory somewhere in China with little or no customer helpline or service if things go wrong.
Some of the own brands can be disguised by the shops for example in Asda their "own brand" was Durabrand or Luxor, in Tesco it's "Tecknika", in PC World it's Advent so their not exactly named as "Asda", Tesco or PC World, but generally it's a brand that you don't see in any other shop and that doesn't seem to have it's own dedicated website.
These own brands also tend to be the first thing that hits you when you step through the door as well, and you'll usually find that the store doesn't just supply the PC under this brand they also have the cheap accessories to go with it under the same brand name, like keyboards, headphones, USB flash drives, etc.
Of course some of the big name brands are made in exactly the same factory but because these are dedicated computer manufacturers they tend to invest more in keeping that side of the brand looking good with a good customer service team. At the end of the day that's their main business so they don't want to damage their primary business.
Also another thing to be careful of, with reviews on the internet of these companies. You may find some people say "I had a bad experience with company XYZ and will never shop their again" you have to be careful with some of these, as some can be genuine, but others can be rival companies deliberately trying to damage one brand to promote their own brand.
Finally don't forget even if the customer service helpline is unable to help you, you always have the help of all your friends here in the CNET community.