The issue here is that what you hear through the TV probably colours the sound a lot, and has a lot of frequencies missing.The reason I'm confused though is that I don't need to generate big volume. I'm only playing at home. I thought an amp and big speaker cabinet was to generate big volume eg for a stage.
If I play a YouTube video of someone playing bass out of my TV, it sounds good. That doesn't have a 12" speaker or massive tube amps powering it.
I don't want to have to plug it into my computer and modify the sounds, that is effects and I just want to learn to play the bass without all that extra stuff for now. Plus my pc is upstairs and I want to practice downstairs in my living room. That is where my digital piano and home stereo are, both have in built amps and line in capability.
Plugging it into your computer to modify the sounds isn't just effects. You will need some kind of amp sim to get even moderately close to the sounds you're hearing on YouTube videos etc. All bass sounds you hear on recordings, from live concerts, all that, has passed through an amp (and likely a cab) which all colour the sound in some way. You don't need to be adding modulation effects, you just need the sound of an amp. If you want cheap, look at the Zoom B1four, and pick one up secondhand if you can. This is a cheap modelling unit that is more than enough for when you're starting out. You can then take the line out from this unit and plug it into somewhere - be that your TV, digital piano etc.
Also, don't expect to be slapping like davie504 for a while - slap is a very hard technique to master. I've played bass for close to 20 years and I'm still awful at it, though in fairness I don't often try and brush up my technique