BT kit isn't normally too bad in my experience, and Linksys is also usually ok. It may be that wireless and/or BT line are both the problem.
RE: Wireless issue, perhaps getting one of the more recent high speed ADSL wireless routers would give you better strength signal and less likely to drop?
I think it is worth spending a little more and ensuring you have a compatible router and wireless card (I would be tempted to add a wireless PCMCIA card to your laptop to ensure it is the same make and standard as the ADSL Router, less potential for compatibility issues then).
It isn't cheap but something like this?
Worst case, just get a compatible 'bundle' (or matching card + adsl router) like this:
I haven't used either but I don't think you can go far wrong with decent brands, a single ADSL/Wirless router and a matching card.