I'll toss my hat into the front to back method for who ever is counting.
My short answer though is Id upgrade both . Asap.
RE which one first?
I've heard very expensive speakers sound not so good on modest front ends, and I've heard modestly priced speakers sound outstanding off a great front end.
In other words, what the speaker see's is the most important thing. The signal quality, and at times, how much there is of it. The speakers needs for power (juice) is always a consideration, as well as is its voice.
What sort of voice & how much juice you want to feed them regularly is going to be your main concern?
Gonna stay SS forever? Wanna try tubes? How about SET?
As signal purity is IMHO 'PARAMOUNT' I prefer the source to speaker plan.
Consequently, less money needs be spent on speakers that way right off. For a good long while too. Ultimately though you'll want to upgrade them most likely.
By that time however, you will have established a far better degree of signal quality, and adding fine speakers will let you have a better feel for what it is you want in a loud speaker by then... Two ways, two and one half... full range... panels.. horns... etc.
I prefer that path versus jumping on expensive speakers and then trying to catch up to them by adding the proper match for them in terms of power amp.
Great front ends will make modest speakers sound great!
Great speakers with modest front ends won't sound like they should or could.
so it comes down to this for me, Do I want a great sounding system now? Or a great sounding system in a year or two or three?
If you're in a hurry... and on a budget too... go front to back. If there's no budget constraints well, have at it all, naturally. I assumed there is some money concerns given the initial question though.
About the only thing one can take from threads like these is the speaker & amp combinations are nearly THE key to a good system. That blend is indeed very very, integral.