Hello! The short answer is there is no one home karaoke system I'd recommend. Just like buying a car there are many factors that go into picking out something that's right for you. The more info you give us about your specific needs the better we'll be able to help you.
Asking for a recommendation is a common question. I suggest you read at some of the other posts. There is a wealth of information here that can help you figure out what's best for you.
In general you need a TV, a device to play the karaoke music and words, some mics, a mixer, and speakers.
I recommend using the streaming karaoke service Karafun. It costs $7 for two days and $10 for an entire month. They have 47,000 songs in their catalog. Their software runs on many different devices. It's easy to use and has some great features.
Karafun outputs to your TV and your AV speakers. Your home AV speakers are fine for the karaoke music but they're not designed to handle the peaks generated when singing. You could damage the speakers. But this setup gives your half of a decent karaoke system.
So for the other half you typically need mics, a mixer, and powered speaker(s) to sing through. You could also route the music through this half of the system but it's not absolutely necessary.
Here are my posts for two low cost solutions
https://www.reddit.com/r/karaoke/comments/pjqnrd/my_recommendation_for_a_low_cost_home_karaoke/
https://www.reddit.com/r/karaoke/comments/smqble/my_2nd_recommendation_for_low_cost_home_karaoke/
But if you wanted something a little better
For mics I like these
https://www.amazon.com/innopow-80-Channel-Microphone-Continuous-WM-333/dp/B0749L15PF
For a mixer I like one of these. They're easy to use and have good echo/reverb vocal effects.
https://www.sweetwater.com/store/detail/MG06X--yamaha-mg06x-6-channel-mixer-with-effects
https://smile.amazon.com/Mackie-ProFX-Mixer-Unpowered-6-channel/dp/B07XC3BHTL?th=1
For a powered speaker(s) there are a lot of options and the right solution depends on your needs.
Speakers
If you want an excellent small profile speaker and are willing to give up having a separate mixer then this speaker with mics is all you need. I've used this speaker and was blown away how good it sounded for karaoke
https://smile.amazon.com/Bose-Bluetooth-Speaker-System-Battery/dp/B078RT7VRZ?th=1
If you're looking for a single speaker, I don't have hands-on experience with it but this speaker has all the features I'd recommend and its's well reviewed.
https://smile.amazon.com/Mackie-Thump12A-1300W-Powered-Loudspeaker/dp/B073V7MKQZ
If you want to use two speakers in your setup I recommend Rockville. I have them and they work well. For home use I'd probably recommend the 10" because it's a little more manageable size but I like the 12" version as well.
https://smile.amazon.com/Rockville-RPG15BT-V2-Bluetooth-Additional/dp/B088ZH5CGH
Here is another style of Rockville that uses similar electronics.
https://smile.amazon.com/Rockville-BPA10-Professional-Powered-Bluetooth/dp/B01C564PZ2?th=1
That's an interesting question. Being able to spend more money opens up more options. Based on my hands-on experience and what I've read from others, here are my recommendations.
Mics - I've had these for two years and I still love them.
https://smile.amazon.com/innopow-80-Channel-Microphone-Continuous-WM-333/dp/B0749L15PF
Mixer - I don't have these but they have the features I recommend. I like using a separate mixer because you can locate the controls in a more convenient location.
https://smile.amazon.com/Yamaha-MG06X-6-Input-Compact-Effects/dp/B00I2J4V5G
https://smile.amazon.com/Mackie-ProFX-Mixer-Unpowered-6-channel/dp/B07XC3BHTL?th=1
Speakers
If you want an excellent small profile speaker and are willing to give up having a separate mixer then this speaker with mics is all you need. I've used this speaker and was blown away how good it sounded for karaoke
https://smile.amazon.com/Bose-Bluetooth-Speaker-System-Battery/dp/B078RT7VRZ?th=1
If you're looking for a single speaker, I don't have hands-on experience with it but this speaker has all the features I'd recommend and its's well reviewed.
https://smile.amazon.com/Mackie-Thump12A-1300W-Powered-Loudspeaker/dp/B073V7MKQZ
If you want to use two speakers in your setup I recommend Rockville. I have them and they work well. For home use I'd probably recommend the 10" because it's a little more manageable size but I like the 12" version as well.
https://smile.amazon.com/Rockville-RPG15BT-V2-Bluetooth-Additional/dp/B088ZH5CGH
Here is another style of Rockville that uses similar electronics.
https://smile.amazon.com/Rockville-BPA10-Professional-Powered-Bluetooth/dp/B01C564PZ2?th=1
To keep things within your budget and still have decent quality I would recommend using your existing tablet/phone/laptop and subscribe to a streaming karaoke service like Karafun. You'll need some available internet access outside but it doesn't use a lot of data so you don't need to worry if you have to use your mobile data.
The Fifine has a lot of good reviews but I have no personal experience with it. If you wanted to use it I recommend getting one powered speaker like this. I have a similar Rockville powered speaker and it works well.
If you wanted to go with an All-in-one I'd recommend something like this. I don't have personal experience with this either but it does have decent reviews.