Any apps already brought via iTunes will not work on non-Apple tablets.
Many of the non-apple tablets are running Android, the operating system from Google. They use Google Store Play.Google.Com or they use their own version of it such as Amazon UK AppStore (links to version for desktop PCs, so you can see some of the things it has and typical app pricing).
Tesco may be launching an Android based tablet very soon... so another one to consider if indeed their press event tomorrow does announce that it is an own brand tablet.
Tablets from HongKong may well be fine, though I would be concerned about returning it if there was a problem.
I would aim to get something with more on device memory, such as 16gb or 32gb, plus as fast a processor as possible, so something like a 1.5ghz or higher Processor, which would be in tablets around the £100 price mark I expect come Xmas. Some tablets can have storage expanded via Micro SD Slot but if they are anything like my Android phone, that additional memory is tricky to get to work with apps, it's more for storage of photos and music.
Amazon Kindle Fire Specs - you will see that on the far right is the first one, which had a Dual Core TI OMAP4 (4430) HS, 1.0 GHz processor. The latest version (far left side) has a Dual Core TI OMAP4 (4470) HS, 1.5 GHz processor. I don't know much about processors but I can tell that the new one is faster.