I would stay away from internet dealers until you become more familiar with bikes in general. It's very important that you have support from a local bike shop that will support your bike with parts and service.
Sorry Stevedahon, I disagree that you have to visit a LBS to make a bike purchase. There are great Internet dealers and poor local bike shops and the converse. Downtube is a very good Internet dealer with quality bikes for the price and they provide good support. Have you ever rode one or read the threads on these bikes? It doesn't matter whether Pat is 1st time or a veteran on the forums, if she buys online then she can have the bike tuned by a good local bike shop that services bikes, if the price and specification are right. The main advantage in using an LBS is one that offers test rides, if they don't then it's pointless. If they do and Pat feels more comfortable with a test ride, then fair enough.
I bought my first folder from Downtube on the basis of this sub-forum and the spec of the bike. It worked out fine and Yan from Downtuve has a very fair returns policy so you can trial never mind 'test' the bike. On that basis the Downtube Mini is a very good contender for Pat because it rides well and folds very small. Another contender that rides well, folds small and is competitively priced is the Dahon Curve D3 3 speed. See:
http://kentsbike.blogspot.com/2007/0...-curve-d3.html and also
http://nycewheels.com/dahon-folding-bike-curve-d3.html
Pat if your local Dahon dealer will do test rides (willingness to varies in the UK) then try out the D3 if they have it in stock. Good folder and also value for money. Don't write off the Downtube Mini. Great review on this forum of it See:
http://www.bikeforums.net/showthread...ompton+vs+mini
Given your preferences stay with the very compact folders.
PS The Brompton is a very good folding bike but much more expensive as a first time purchase unless you aren't constrained by or budget conscious. Let us know how you get on and good luck. Whatever you decide on we all agree you will never look back with a folding bike. 'Once in the fold you will be sold!' :-)