Hi Sue !!! Congrats on joining the board !
You are not asking an easy question at all. So much actually depends on your personal tastes. I'm going to guess that you want to get you base tone right before moving on to modulation/delay/reverb effects, so I'm going to stick to dirt pedals.
There are two ways of using drive/OD/dist/fuzz pedals with an amp. Firstly, you can use a clean amp sound as a tonal base, and then use pedals for all your drive/gain sounds. The clean channel on your Valve King would be the best for that.
Secondly, you can use an already overdriving amp, and then push it further with pedals - Your Tiny Teror would be the clear choice for that approach, I think.
I have used pedalboards both ways. Some pedals work best into a clean amp, some work best into a driven amp. As a general rule of thumb, I would say that Tube screamer-type pedals work best into an already cooking amp. Fuzz and higher gain pedals usually work best into a totally clean amp. In my experience I have found that there are more pedals that prefer a clean amp than those which like a driven amp.
OK, after all that, I am going to suggest you try/get an MI Audio Crunch Box (M&M music, Soton). Reasonably cheap, true-bypass, awesome, high gain pedal - Marshall-style. I hardly ever hear of anyone being disappointed with one. I love mine. BTW, this pedal is best into a clean amp, but still OK into a driven amp.
From the bands you have mentioned it looks like you would also appreciate a moe vintage sounding Marshall-type pedal, one that gets Plexi-JCM800 type tones (70's-80's). I'd recommend either a Himmelstrutz Fetto (very expensive - but superb !), or a Menatone King of the Britains (I have one of these in the post - you can try it out when I get it, if you like), or a Wampler Indyguitarist Plextortion. None of these is "better" than the other, all just have their own character. BTW, the Plextortion is the cheapest !
It would help me, and others, focus our suggestions if you can tell us exactly what type of tones you feel you are lacking, and whether you are going to play through a driven amp, or a clean one.
Alan