Can someone recommend a cheap but decent mic with amp/speaker? (x-post several subs)

First about me: Male. Mid-thirties. Completely self-taught. Never done professionally. I don't want to overstate myself, however in my younger days I would have called myself very or even extremely good. Despite thinking the show is dumb, if American Idol had existed when I was in my teens/early twenties, I would have tried out and think I would absolutely have made it on the show, possibly even advanced. Big Tool fan and when I used to still practice regularly could match Maynard note for note and sometimes even surpass him (though I could never get down his version of fiddle and the drum. I think this may be the most challenging song for me I have ever come across.) Just to give an idea of both skill and style. I also love Chris Cornell, Mike Patton, Freddie Mercury, and basically anyone rock or heavy rock who I think is at the top of their game vocally to try to emulate them. I'm out of practice but this was something I formerly absolutely loved to do. I'm graduating college (I never got serious about it til I was 30 :/ Better late than never I guess,) and now that I will have some free time again, I'd like to get back in to it.

What I'm looking for: I would like a mic and amp/speaker just so I can hear myself more accurately in order to improve more and tweak little things that might otherwise go unnoticed. A combo kit (mic and speaker included together in one purchase) would be highly preferable, but is not a must. The only things that are absolutely necessary are a mic, speaker/amp (I don't know the correct terminology) and a way for them to connect. I mic stand and pop-buster (used them in the past and really liked them) would be considered a bonus or luxury but not required. I don't plan on performing (maybe karaoke) and live in an apartment so it only needs to be powerful enough that I can hear myself. Doesn't need to be super high-end by any means, in fact, the cheaper the better, but still good enough to be worth owning. I'm hoping for under $100 but I'm flexible to an extent if I have to be (in other words if what I'm looking for isn't even available for that price.)

I come here to ask because I'm sure there are so many variables of different types and options and tiny little nuances of different systems that can be considered when looking for something like this, and to be perfectly blunt, I just don't feel like fucking with having to learn about all that. I just want to sing. Honestly I was hoping someone would just tell me what to buy, or give a small amount of options for me to pick from so I don't have to wade through the minutiae just to add a single item to my Christmas list.

Thanks all.