You can do either. There are floor protectors for spikes (there are plenty of brands and choices - https://www.amazon.com/Speaker-Spikes-Protectors-Isolation-Turntable/dp/B07C2KK96B
) In the case of my main system, I have an area rug that is not super thick and my speakers came with spike like feet (4 of them and they are not as pointy as spikes and the speakers are not rectangular) which are adjustable. I have floor protectors on the front ones and on the back ones I took carpet remnants left over from the house install and they are a bit thicker and I have them on the remnant (which is on top of tile. I have a couple of other systems where I have real spikes on top of carpet and padding and I just put the spikes into the carpet. The idea with spikes is to acoustically couple it to the floor. I don't drive myself crazy if there might be a slight difference doing one or the other. I'm one to put a system in a real world living space and take care of the bad problems (e.g meausre response with a RTA and have sound treatments to mitigate/tame the bad problems). I also have a couple of integrated AC systems, including the main one. Ideally is theory I'd love to have a nice dedicated space for HT and then another room designed only for 2-channel. It just wouldn't be practical for me and be able to use my house as living space. I use my main system mostly for music but it is so good on HT (7.1.4 Atmos with a Power Sound Audio S1500 for the ".1" channel - https://www.powersoundaudio.com/products/s1500
), so here are times when I enjoy it for HT. I have another integrated system in an average sized bedroom that I use mostly for HT and TV. It still sounds very good for 2-channel and once in a bit I'll listen to it either for myself or when someone is over and interested in hearing the components (I have a preamp with HT Bypass and a nice amp for 2-channel). Sometime in the near future, I'll be upgrading the UHD TV in that HT system in the bedroom (probably for this year that's my major audio/video upgrade) and getting another UHD player (probably the Panasonic UB9000).
So the advice I would give is get something within your budget that will result in something better than what you have and that you will be happy with and can live with for a bit. There's other things I want to do but like everything there's budget constraints and I have to have other things done (non-audio) before I can do the audio. Sometime within the next year or so, I will get my (master) bedroom painted and after that the living room which connects to the dining room, kitchen, downstairs hallway and up a long flight of stairs to the bonus room. After I get the bedroom done, I'm going to take the main system projector and move out the bedroom system one. So that system will be upgraded. I need a new mattress so that will get taken care of first. Then once the main system projector is gone (which sits on a pole hanging behind my listening position), I will likely get a bigger screen (I have a 100 inch one but will end up with one more 4k friendly and either 110 or 120 inches, assuming the latter will fit between my height channels which it should and I plan to try and mount them a little different, if possible, before the room gets painted) and would like an ultra short throw projector I can stick behind the center channel. I'll have to see about pricing and other factors (but it would be nice to have the pole gone). So tackle whatever is in your budget in a priority that makes sense for you and will result in something better than what you have.