i'm reading through this thread and i have to point out a minor error. Tony Miller's #4 is not a paddle strop but a simple 2.5" wide hanging strop without any linen or fancy hardware. I think it runs for about $22 give or take. If you want a 4 sided paddle strop Tony also offers those. He had two current models: one with all 4 sides meants to be pasted and another which is meant to have 3 sides pasted and one side dedicated for daily stropping. he also offers various 2 sided paddle strops. You can check it all out here:

http://shop.thewellshavedgentleman.com/

pastes are used to refresh a dull edge/achieve the super sharp and smooth edge

if this is something you can really see yourself pursuing (and i bet it will be since its kind of addicting) then i'd go for the hanging strop first as its more fundamental, then add tools like paddles and hones to your arsenal once you get the basics down

another option is to get a paddle strop with both a finishing side and a pasted side (chromium oxide most likely) that way you've got a daily strop and a way to refresh the edge

send Tony an email, he'll be able to help you make the choice that fits you