I have searched and searched but everything recommended in articles is a modeling amp. I just want something with good tone and more than three controls that I can run effects pedals through.
used Peavey Bandit comes to mind.  if you can stretch the budget a little a used version 1 Peavey Valveking would be an option as well. 
All tube, more than 3 channels and <$200? Not gonna happen.
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Quote by Axelfox
Wash cars, mow lawns, sweep floors and come back when you have some more $$.  Essentially all the low end practice amps at that price are SS with some modeling.  A Roland Cube is decent, and in clean JC mode it takes pedals well.  Crate maybe??  Used Super Champ in the clean channel takes pedals like a Fender Blackface.  When bottom feeding on price, you have to be willing to make a lot of compromises. 
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

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Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
Last edited by Cajundaddy at Mar 15, 2017,
Do you have a cab? If so, the best I can think of is this (at @$299):

And their newest (@$149):

Yes, they are solid state. No, they're not modelers. Yes, they take pedals well.

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Quote by T00DEEPBLUE
All tube, more than 3 channels and <$200? Not gonna happen.

The only way wold be to watch the classifieds like a hawk, and wait for someone who needs to get rid of an amp quick for cash.... seems to happen a lot to musicians . I've gotten a blues jr, xxx, and Ultra combo for $200 or less CAD, which is about $150 USD. And I think he meant 3 knobs, not channels
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On the cheap $90 Nano Legacy (whatever flavor). Cab under $100. Not gonna be great but in budget. Or go used for a bit better. Mono price makes a cheap combo. VHT has a combo under $200. The fact your gonna use pedalboard makes it a bit easier .  
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Quote by T00DEEPBLUE
All tube, more than 3 channels and <$200? Not gonna happen.

he said controls not channels. guessing he means for EQ and gain
It looks like OP has edited his post and removed the "all tube" requirement. So I guess solid state is acceptable? But $200 is still not enough to get one with an effects loop unless it's used. The Orange Crush 20RT is around $189 new and it's a great, 2-channel practice amp with built in tuner and reverb. But it's not going to have an effects loop. If it's a must, you could get a used Peavey Bandit or Orange Crush 35RT. Those are the only non-modeling amps I remember right now.
Last edited by meateatingvegan at Mar 16, 2017,
diajkeene DIME D100 is in your budget if you play rock/metal... Its 2 channel + 1 Gain Boost... It feel like 3 Channel amp...