I’ve got the same tellybox and wish I’d got it for £360 now – ace price! I didn’t bother with the WiFi dongle though, just moved my router and hard-wired it in and most times I get no problem and can watch anything on iPlayer in normal resolution and occasionally HD too. My broadband is about 3mbs apparently and luckily the telly sits by the main phone line. I got a USB WiFi adaptor for my PC instead.
Strangely, what I did notice is that I now get much better connection speeds with the router in the main BT line-in socket rather than a phone extension socket (download speeds now ca. 400kbs instead of 150kbs) so it might be worth trying that.
My router is nothing special – a 54mbs one which is still way faster than the broadband connection so I doubt thats your issue.
Only other thing I do is if the connection is a bit clunky I just switch the router off and on again. Seems to help clear the decks or something!
Might also be worth running a broadband line test to see what download speed you’re actually getting – e.g. http://www.broadbandspeedchecker.co.uk/%5B/url%5D
best of luck! Andy.
Edit: hadn’t noticed the bit about iPlayer working fine on your laptop – that does seem odd..