What an exciting upgrade! I don't think you'll regret it one bit honestly. You have an amp that can stick with your system for pretty much any set of speakers you might throw at it. Plus if you'll have the ability to tube roll, run triode or ultralinear, could expand to monoblocks if you wanted to get really crazy. I think you can just consider that part of your system "done."
Speaker cables and interconnects are obviously a disputed topic. In my opinion, they are well worth investing in. Your speakers and sources may somewhat dictate how revealing cables changes are, but I'd expect differences - especially when moving to big differences in designs.
In an ideal world, I'd say full loom of the same company is the way to go, but it's also generally expensive and unrealistic to do so. I do know several people who have preferred brands for power cables, different preferred brands for analog cables (inter + speaker) and another brand for digital cables. And I would say don't look for a best cable - synergy and personal taste are big inputs here. I don't think one specific cable is more important than another, but if one cable is holding back the whole chain it might be harder to tell. Same as source equipment.
To get started on a more affordable path, I would recommend looking into Zu's ebay sales. I do really like their Mission interconnects, and at the prices they can go for on ebay, they are well worth it and an upgrade from BJC in in my opinion. I'm not as keen on their Libtec speaker cables, but I do still have my set in case I want to mix things up.
I also have really liked what I've heard from Wireworld, although I'm not as keen on their Silver/Copper blend option (silver eclipse?). If you have good gear in place, find cables in the budget you are comfortable with, and then I'd say stop messing with gear changes and just buy/sell cables when you have an itch to try something new. Some high dollar stuff can be great, but there are some affordable gems out there as well.