Which model soundbar?
Turntable without a built in phono preamp > RCA cable > phono preamp > RCA to 3.5mm aux cable > Soundbar aux input.
RT81 to Spinbase, you can use either phono preamp:
However the older RT81 is not worth buying anymore since the newer improved RT82 for $50 more adds a $100 increase in component and performance value since it adds the new optical sensor speed controlled motor for lower wow and flutter and speed variation and the speed won't drift since the senor is monitoring the speed 400 times a second. Connect the RT82 to the Spinbase PHONO input. Pass on the RT83 since the cartridge is not any better.
For the speakers consider that for $85 less you could get a pair of compact 4" mid bass driver speakers that gives you stereo separation, imaging and sound stage for better sound and performance than the single SpinBase.
4" Klipsch KD-400 $159 powered speakers plus Art DJ Pre II $65 phono preamp that should be better than the one in the RT81 or Spinbase.
Or for $20 less than the Spinbase, 4" Klipsch R-41PM $279 have a built in phono preamp.
Stylus upgrade https://www.lpgear.com/product/LPGCFN3600LE.html and double check the cartridge alignment.
Phono preamp upgrade https://www.amazon.com/ART-II-Turntable-Phono-Preamplifier/dp/B0777NFCC5 from the basic $15 value phono preamp built into the turntable, set the switch on the back of the turntable to Phono when connecting the better external phono preamp.
Onkyo TX-8220 $199 and Yamaha A Series $299+ have a built in phono preamp to start with.
Or if there is also a TV in the room optionally an AV receiver with 4K HDMI switching starting at $269 plus a separate $65 Art DJ Pre II phono preamp. Or an AV receiver with a built in phono preamp starting at $349.
Or for used options what is a nearby zip code I can search for you? Reply here or chat or message.
Well, if you gave me $1000 for a system, here is what I would get:
https://www.fluance.com/rt82w-reference-high-fidelity-vinyl-turntable-natural-walnut
https://www.musicdirect.com/equipment/speakers/wharfedale-diamond-225-bookshelf-speakers-pair
Better turntable, better speakers, better amplifier. $900 total.
If you need the amplifier to be compact, then switch the Yamaha for these two things:
https://www.amazon.com/LOXJIE-MA12070-Headphone-Amplifier-Bluetooth/dp/B08J7Z8TN6
https://www.amazon.com/ART-II-Turntable-Phono-Preamplifier/dp/B0777NFCC5
$840 total.
Which model tube amp?
You need a phono preamp somewhere in the turntable setup.
A phono preamp does not just boost the phono signal, it applies the RIAA EQ curve. https://www.audioadvice.com/videos-reviews/what-is-a-phono-preamp
If the phono preamp in the RT81 is working fine then don't bother changing cartridges. If you want an upgrade it's easier to upgrade just the stylus to the https://www.lpgear.com/product/ATSAT0095E.html so you don't need to do a cartridge removal, installation and alignment.
The phono preamp in the amp may not be any better than the one in the turntable. If you really need to boost the level of the turntable output past the level of phono preamp in the turntable or the amp then get a phono preamp with adjustable gain https://www.amazon.com/ART-II-Turntable-Phono-Preamplifier/dp/B0777NFCC5