Naturally, my thinking will contradict Twl's almost to the letter. (It's OK, he's used to this by now :-)
It looks as if you are intent on keeping your amp, and also your speakers. If so, I would say to upgrade the amp first, as it is the last link in the chain that you are considering modifying.
My logic is thus (as I have posted before):
In choosing whatever changes you decide to make ahead of the amp in the system, you will have to audition the results through that amp (and speakers). There are a couple of interelated factors to consider here. First is the transparency of the final links in the system. If the amp mods make it more transparent, then it will be easier to hear and evaluate changes made to the front end components when listened to through the updated amp.
Second is compatability. Whatever balance of qualities pleases you most, if you make your front end choices based on the amp's current sound, and then change the amp later, you run the risk of having a mismatch revealed too late in the game. You have more flexibility and certainty in modding the amp first, then determining the front end changes which will work well with it to create the overall sound you want, with no late surprises.
Based on this logic, here's what I would recommend:
There is no sense in playing around with different tube types before you get the amp upgrades done. Do that, and you may forget about the tube-rolling urge, but if not, you can try that next.
Once the amp is done, focus on the speaker cable choice. The amp and speakers are staying in the system without further changes at that point, and the amp/speaker cable/speakers subsystem will be employed to audition everything before it. The choice of speaker cables is most dependent on the partnering speakers and amp, not the front end sound (especially true in systems with multiple sources, but still true in principle for you). Get this cable optimized next.
Once the amp and speaker cables are done, I would either do the player mod, or better yet, try the power conditioner, and use it on your front end, not just the amp. If you like what it does for your digital, you may decide to forego this mod (this is where I have found balanced power to be most effective). Even if you don't like the results of the PLC on your amp, you may keep it just for the digital. Then get the player mod done if you are still convinced of its worth.
Now that everything else will have been put in place, it's time to wrap it all up by choosing your ultimate interconnects. With the sound of your front end digital subsystem and amp/speaker cable/speakers subsystem updated with mods, new cables, and power conditioning, you can now choose the best IC to connect them and complete the sonic picture accordingly to your taste. (Normally, I would recommend upgrading the IC running to the amp before messing with the front end stuff, so as to make it more revealing of choice options there, but with no preamp, you don't have one IC common to different sources, so you might as well just optimize it for your one source.)
Once you have done all this, sit back and see if you still feel the itch to try a sub, as your bass may have improved somewhat in the meantime. At least if you do audition subs at this point rather than earlier, you'll know whether one can actually improve upon the final configuration of your system, rather than simply providing a band-aid or distraction which wouldn't have been needed (or maybe screw up the synergy) farther down the road.
It's not that I don't understand the school that says 'garbage in, garbage out'. It's that the goal isn't necessarily the most listenable sound today, but trying to put together an entire system with some semblance of a basis in logic and accuracy of the auditioning process. Ideally, I think that means choosing speakers first and working roughly backwards from there by subsystem, particularly in rigs where there will be multiple sources, all of which must be listened to throught the same final links, but which are chosen independently of each other. But it's not always possible to proceed in the ideal fashion, something I've had to contend with lately, after pretty much staying on schedule for a few years.
But that's another story. Good luck however you approach things!
