This seems to be more about playing out and implies that you are going to play amplified. If you're going to play in pubs you will definitely want to be heard among the people drinking/eating/talking.
What are you going to play through? Amp? PA? House PA?
Unless you are going to rely on house PA systems (and the people who run them) you're going to have to buy some amplification system, either amp or small PA. You're likely going to want something that will enable you to optimize your sound together, like one of the many small PA systems available.
There are pros and cons to both approaches. . . and stuff you'll need, cords, DI box for you if you're going to use a transducer pickup, mic(s). . . There are lots of questions and considerations and, if you don't have any experience with sound reinforcement, you're not really going to know what you're doing and why. A small PA is the most flexible for solo/duo. You usually get 2 speakers which will help you fill a room with decent sound and some options.
I have this, perfect for solo guitar/uke/vocal It cost me about $600.00US, plenty loud, good sound, and options.
http://www.yamaha.com/yamahavgn/CDA/ContentDetail/ModelSeriesDetail.html?CNTID=36692
Here's Carvin, mail order, good value, lots of folks swear by them.
http://www.carvinguitars.com/products/group.php?cid=10
http://www.carvinguitars.com/products/group.php?cid=101
Peavey, also good value, lots of folks use 'em
http://www.peavey.com/products/browse.cfm/action/list/cat/398/begin/1/PViSeries.cfm
http://www.peavey.com/products/speakers.cfm
So, while you may be thinking about a new uke, and the pickup is an important consideration, you should really think about amplification. As far as what size uke, doesn't really matter. Play what you like.