Years ago, I replaced the stock speakers in a JVC PC-55 with some Diamond Audio D151 component speakers, and I filled the speaker boxes with some polyfill batting. The difference in sound was mindblowing. Speakers on a boombox, generally, are the weakest link in the sound chain. I would imagine there are some boomboxes where one would be hard pressed to actually improve (instead of just changing) the sound.
Car or home choice does not really matter in my opinion. Staying with the same ohm rating is considered by many to be the safest way, but going with a lower ohm rating can work too. Member Cpl Chronic went from 6 ohm down to 2 ohm (Infinity car speakers) in a Sharp GF-777 and seemed to have good results. The main thing is to not go to a higher ohm rating. Doing so will make the amp work harder and will more than likely blow the amp after a while.
Also, I would suggest looking for speakers with the highest sensitivity rating. Moving more air using less power is a good thing.
