Most adapters are plug and go, the only ones that may prove a bit more
of a challenge are those with Broadcom chipset. but even those tend
to be fixed after an update via cable ( does mean running an ethernet
cable temporarily ).

The Linux Compatibility List site is a good place to go for all sorts
of hardware questions - http://linuxhcl.com/ and you can specify
Ubuntu in the search too.

Personally I've found ZyXel USB adapters to be reliable and 'just
work'.

One point to mention - Wireless 'N' adapters are more of an issue than
the 'G' ones but you do tend to get a greater range with them. Depends
on the distance between router and PC whether you need to consider 'N'
devices.

Another option to consider for a fixed PC is ethernet over mains
units. These are pretty good and have used these quite a bit too in
situations where wireless is a problem.