I'm from UK, so my pick would be:
1st leg: Andrea Lynch
2nd leg: Kathy Cook
3rd leg: Paula Thomas
Anchor: Sonia Lannaman
Andrea was a decent starter, has the 2nd fastest 60m by a Brit all-time, and had a best of 11.16. Kathy Cook holds the British record in both 100 and 200, but her 200 record is arguably better, and so should have the longer 2nd leg of the relay. Paula Thomas was a 11.15/22.69 sprinter. Her decent 200m time shows she'd be a decent bend runner. Sonia Lannaman has several windy and/or handtimed sub-11 100's to her credit and ran the anchor for the NR, so she's my pick for the anchor on this dream-team.
I reckon this team would be capable of a time around 42.20 at best. The NR team of Lynch, Cook, Hunt-Oakes, Lannaman ran 42.43, so the only difference between both teams is Paula Thomas running instead of Heather Hunt (11.15 to 11.20). So, if the "dream team" practiced on changes and had a GDR team in the lane outside them and a US team breathing down their neck, I reckon 42.20 is possible.
As for British men, these are my picks:
1st leg: Jason Gardener
2nd leg: Dwain Chambers
3rd leg: Linford Christie
Anchor: Mark Lewis-Francis
Jason is a sub-10 man at best, holds the British 60m record and is a reliably fast starter. Dwain is another sub-10 man and is (equally) the fastest UK man, and so should have the longer 2nd leg. Christie is a 9.87 man and also has a 20.09 200m to his credit, so would be a valuable bend runner. Mark Lewis Francis is definitely on anchor - he doesn't know any other leg, plus his pick-up is amazing.
I reckon this team could do 37.40 at their absolute best. The current NR is 37.73, and that was run with Devonish and Campbell in the team - my dream team has MLF and Christie, and the difference in PBs between Devonish & Campbell and MLF & Christie is 0.33. They could arguably go faster, because at the time the NR was run, Chambers was not at his peak (he knocked off 0.10 since then), so they could potentially go faster... scary thought!!
Awaits barrage of criticism from American track fans...