Polyvinyl acetate otherwise know pva (wood glue) is gonna be your best bet for 99.9% of wood gluing applications. Get the most basic stuff you can find. Here in North America we like our titebond original (not the water proof stuff, that's for outdoor basses
) Generally speaking If the joint is good and the glue is applied evenly, all that is needed is to hold the two pieces together, ie there's no need for clamping pressure to achieve a good bond. The reasons we clamp are to hold things together not to apply great force. That said there are exceptions but that's a lot to go into here.
Also worth mentioning, is that two pieces joined correctly on their flat/quartered grain won't break along the glue if stressed. The wood will, because a pva joint in wood is typically going to be much stronger than the wood around it.
This happens because it gets absorbed into the wood and creates an all around more dence material.
As for a plug it's kinda a tricky thing imo. You want a snug friction fit around the perimeter which usually means you can only insert it once. Generally this is a no no in woodworking as we want to test our joints before applying glue. That said if you get a snug fit and than add glue (pva) to that equation the only clamping you'll need is to get it in as it'll now be an even tighter fit. For this though you don't need a clamp you can use a mallet. Once a tight fitting plug is glued it's not coming out, no clamps required. Again it's a tricky thing if you've never done it before and as such I'd say try it on a test piece first, maybe try it a few times. Get comfortable with it first. Also being as this is what it is I'll say measure twice cut once.
(it's ok we all mess this up now and than)
And in a world of boutique 'hand'-painted/printed' stomp-boxes... elegance in raw simplicity. 
