My current amp is a Peavey 112 Ultra, but it's getting quite old and beginning to act up a little bit at times, so I'm considering replacements for it when it finally decides to kick the can. I'm looking at modelling amps, mostly because I don't have to money to buy all kinds of fancy pedals and whatnot, so having all those effects and presets built-in would be of a great advantage to me.
Musically, I tend to play heavier, classic stuff(Metallica, AC/DC, etc), along with more modern bands, like Shinedown, Rise Against, and the like. The two electric guitars I own are a Fender MIM Strat and a PRS SE Custom 24, the latter being the one I play the most.
My budget is between $200 and $300, USD. I'd prefer a 1X12, but if there's another noteworthy amp that's worth considering, feel free to put it up for suggestion.
I'd get a Peavey Vypir. The Mustangs just fall short of it IMO.
Get a Vypir 75 or a Vypir Tube, which aren't made anymore, but supposedly the best of them.
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dude take your Ultra to a tech and have it looked at. chances are that it just needs a little tweaking or even just new tubes.
Best case your Ultra needs new tubes (probably power tubes), worst case you might need to have the caps replaced.

Anything other than that (which is all standard tube amp maintenance) is very unlikely. Old MIA Peaveys are pretty much indestructible.
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Ibanez RGA42E
Ibanez S420
LTD H-301
Ibanez RG520
Peavey Predator USA
Douglas Grendel 725
Line 6 Pod HD500X
Yeah, definitely just fix and maintain your Ultra. Don't take a step down to a non tube amp, unless you have to.
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I agree with these guys and I own a Vypry Tube 60.

Going for a power tube swap first would be my bet. That way, even if you do end up getting a new amp you can at least keep the new tubes you just bought or sell your Ultra with 'new tubes' which would be attractive to some. Maybe pick up at least 1 new preamp tube as well like a JJ 12AX7 and try swapping it around.

That said - if you still want to move onto a modelling amp for the reasons you provided I DO highly recommend the Peavey Vypyr Tube series. Vypyr 60 or 120. They have a tube power section (based on the 6505) and analog amp modeling. I love mine.
So, as the general consensus is that I should just replace the tubes, I think I'll go with that. However, I've never actually bought new tubes before, so I need a little help choosing some. The tubes that are currently in my amp, according to a quick Google search, are JJ Electronics 6L6GC power tubes. Should I simply get a new set of these, or is there a better option for roughly the same price?