Welcome to the tree
and to the very addictive world of cloth!
We have easyfits here they are fab! If you like those you could look at trying a Bumgenius they are similar.
Blueberry Sidesnaps (BBSS) are very good as are Wee Notions SS's, I'd avoid anything like those in One Size at this point, I just couldn't get mine to fit when he was small.
I've not heard of a Tots Softee, I think there is a Lollipop one though, this might be what you have ... I did try one but because they are made totally from Microfibre I found the wee just squeezes back out like a sponge so they weren't much good, same goes for Tots Fluffles or anything made of Microfibre, Bamboo is much better, the Tots Bamboozles are great, either the old type or new Stretchies, they will seem a little bulky on a 6 week old but he'll soon grow into them, Sz1 should last you a good while 18-20lb or so.
I found that 2 part nappies were best when Rufus was very small, infact it's only been the last 6 weeks or so that we've been using All-in-Ones and Pockets without leaking around the legs ... with runny newborn poo I did find that I was happier with 2 parters, the best wraps I have found are Thirsties Duo (you can get velcro or popper fastening) you can get these from Peachy Tots or Kittykins, they have gussets at the legs so really keep in those explosions! We've never had a leak with them. Little Lambs Bamboo are also a good option for basic nappies.
There are also lots and lots of 'Pretties' you can get with patterns or in lovely hand-dyed colours, again I'd look on the classifieds for these ... Dunk n Fluff, Holden's Landing and Fluff & Stuff are good brands to look out for.
Check out the Classifieds as you could pick up things to try very very cheaply.
Hope that helps, I'm sure some of the other ladies will be along with more suggestions soon!