Since your amp is
an EL84 based amp, I would recomend the JJ EL84's as they have a very proven track record of being reliable and sounding good -- This is just for the EL84 power tubes.
Since it doesn't sound like you're really wanting to dive into the whole tube swapping thing, I would also recomend Bob @ EuroTubes as mentioned earlier. Just tell him what you would like to achieve, and he can put together a nice total package for you that will help you get closer to the sound you're looking for. The only "bad" thing about Eurotubes is that they/he only offers JJ tubes.......which isn't bad in it's self, but there are a lot of different brands out there that sound better IMO.. BUT, as I stated above, you can't go wrong with the JJ EL84 power tubes.
Typically Mesa's have a fixed, or non-adjustable bias for the power tube section, so that you shouldn't have to worry about having your amp re-biased (I would call Mesa just to be sure though)
While we're on the subject of powertubes,.... depending on how much you play (Gigging out every weekend?, Just jammin' once a week in your basement??) you should typically change your powertubes about once a year.....give or take depending on the amount of use the amp is seeing. If you're just playing at home in your bedroom using minimal volumes, you're barley getting into the power tube section of the amp, and they will last a lot longer than if you had the thing cranked to 10 all the time jammin' with a band.
Preamp tubes will last for quite some time (years typically), unless they actuall just go "bad".......which you'll know most of the time but the amp sounding really bad, or not working properly.
How many tubes are in your amp (Small/large??) the small ones are your preamp tubes - 12AX7's, and the power tubes are the larger ones (all though EL84's arn't really that much bigger than the pre's
)
If you look on the chassis of the amp, the tube sockets should be marked in some way or another like : V1, V2, V3...and so on. If all of your tubes (Both pre's and power's) are in a single line across the chassis, then PI tube will typically be the one next to the power tube. The preamp tube that is furthest from the power tubes (The 1st one in the line) would typically be "V1" which controls the first input stages of your channel(s) -- This is a single channel amp correct?? The V1 slot will have the biggest effect of all the preamp tubes on your over all sound/tone......so it may be worth it for you to spend a few extra bucks on a "good" tube for that slot. "GOOD" is very subjective when talking about preamp tubes so take that for what it's worth
Some of my favorite current production preamp tubes are:
GT12AX7-M (Mullard reissue)
Tungsol 12AX7 reissue
EI 12AX7-G (Gold) ---- These three can be purchased for under 20 bucks ea.
Then you start stepping up into the Mullards, GE/Jan, Phillips, Brimar, Bugle Boy.......and the price starts going up from there
But as I said, you probably can't go wrong with a EuroTube package from Bob. It will make a big difference in the sound/tone of your amp, and I think you'll be very pleased with the change.........especially if you take the time to talk to Bob and tell him what you'd like to achieve and what you don't like about the tone of the amp now.
More Power Tube Sound - The only way to get more of that "power tube sound" is to crank the amp up and bring the character and overdrive of the power tubes into play --- Most of the time, unless you're playing in a loud band, that's just too loud for most folks. The fix would be an Attenuator. My personal favorite is the Weber Standard Mass, but there are others out there that work well also such as the THD HotPlate. These will allow you to crank your amp to the moon so that the power tubes are in full play, but you can control the actual speaker volume through the attenuator (It basically absorbs the energy/power coming from the poweramp section of your amp).
Crap this was a long post.
Good luck!
Rick