Looking for economical options for better TV sound

[auujay]

I have a weird "problem" (because I am cheap and trying to re-use components). Let lay our the problem, I have a TV in the basement that is only used while on the treadmill. We just use the speakers that are on the TV but they suck and sometimes struggle to get loud/clear enough over the sound of the treadmill when running on the treadmill. The TV is basic with only HDMI and TOSLINK outputs (I am not running a receiver down here, just streaming shows directly from the TV so that is the only audio source). I also don't really have enough space for a dedicated soundbar (the TV is wall mounted with other tables/desks below it) but I imagine I could find space for a bookshelf or center channel style speaker.

Given this is really only used for watching TV shows while working out, I want to be as economical as possible but I want better/louder sound from the TV.

1. Should I be looking for an all-in-one solution, some sort of powered speaker that can take HDMI or TOSLINK?
2. Maybe get a cheap amp with digital input and hook it up to some new speakers
3. Get a cheap decoder for the HDMI or TOSLINK to analog, feed that into cheap amp, then into some speakers (or use the cheap decoder into some cheap powered speakers)
4. I also have some old 3 way speakers in the same space but they are part of another system, what happens if I hook these up to a small amp from the TV but are also wired up to another amp? I would run both amps/signals to these same speakers at the same time...

I would love feedback on recommended approaches or something else I may be missing. Also open to specific suggestions too.

 

[auujay]

Checking the TV's output settings, the only option seems to be PCM. There are some Dolby formats that are greyed out (maybe they are only available with HDMI connections when they are made or only with compatible Samsung soundbars).
If audio is coming out as PCM, does that mean I just need a simple DAC to convert it to RCA rather than converting from a surround format? It seems like some of the cheapest TOSLINK devices warn they can play stereo audio from TOSLINK but not surround. (https://www.parts-express.com/FiiO-D03K-Digital-Analog-Audio-Decoder-230-120 vs https://www.parts-express.com/Audio-Converter-DAC-Switch-2-Toslink-2-Digital-Coaxial-to-Analog-Out-with-Toslink-Passthr-180-1141)