On the bass clarinet. I went extremely low end, just try it out. It is a used Busher (sp!), which, save for a slightly moldy smell, has no other major difficulties. The next stop is a new mouthpiece (the one on hand is a stock piece that came with the clarinet), which brought me to your site. I'm inclined to call/write the first fellow you mention (McClure, or something close to that) and get an S2. Still advisable, or are there other recs that have come to the fore? I can swing the price (though it will be more than half of what I paid for the clarinet), and I know well, from my tenor, that the mouthpiece opens up new worlds. I need as well a new ligature. Recommendations here?
So to answer your question about the mouthpiece, as you can imagine, it's a very personal quest. And by "Personal" I mean, your mouth is different from mine is different from anyone else's -- and that's where mouthpiece recommendations begin to fall flat. You want a mouthpiece craftsman who can -- either through trial and error, or through voodoo -- pick up on your cues and make you something you can easily play on. Those cues are successful inasmuch as you are able to accurately describe what your difficulties are (or what you like) about any given mouthpiece. Think about how resistant it is, or how it responds when articulated loudly (or softly), if it is able to give you a pure (and unfuzzy) tone in all dynamic levels, if you can move easily between registers, including extreme register leaps. Stuff like that will help them help you.
There are many manufacturers/refacers out there who are good, or so I'm told. Walter Grabner, Clark Fobes, and McClune are the three I hear most about.
Ligatures, well, I think they make little difference -- I have a rovner I have used for about 20 years. I like it because when I sit on it, it doesn't break. :)