An almost 'impossible to answer' question given the way you worded it.
If I understand it correctly, you wish to spend $500 on speakers for an amp that costs $90 and the most positive of reviews for the amp on Amazon are about how fast customer service gets back to you when the amp craps out, which it seems to do often enough.
So, don't go overboard price wise with anything with this amp as your system base.
First things first, it sounds like you may need a phono preamp for your TT with this amplifier, unless your TT has a built in phono preamp.
The Keiid is a 40 wpc amplifier. No idea over what frequency the wpc were measured, so no idea if you have 40 wpc continuously available to you. Also, no idea as to what type of music you listen to or how loud. I have never heard a Keiid product, I am shooting in the dark.
I would limit the speaker purchase to $200 and go for something like these:
https://www.musicdirect.com/speakers/wharfedale-diamond-220-bookshelf-speakershttps://www.soundstagehifi.com/index.php/equipment-reviews/911-wharfedale-diamond-220-loudspeakershttps://www.whathifi.com/us/wharfedale/diamond-220/reviewWharfedale makes a good product. You would most likely keep these if you upgraded the amp.
Keep in mind that they are only going to play so loud, but they will sound nice. You are not going to get all the subtleties that are available to you, but you will enjoy what you do get.
I have setup some inexpensive systems that sound real nice. These days, I suggest powered speakers (Kanto) and TTs with built in preamps AT or Music Hall). For small apartments they do very well. In bigger spaces not so well.
Good luck.
Rich