$30 total for the Fire 7. https://www.amazon.com/dp/B01GEW27DA/ref=cm_sw_r_cp_apa_yVezzb14RTXSN
The Fire 8HD is going for $50 instead of $80 as well. https://www.amazon.com/dp/B01J94SWWU/ref=fs_ods_tab_ds
An mp3 player that runs android and supports the google play store is required. (another option is to get a cheap phone or tablet, like a kindle fire). Then you install the amazon music app on the device from the play store (or from the amazon app store on a kindle fire). Once the app is installed and your device is connected to wifi you can just run it and stream music or download it for offline play.
In order to get music to a stand alone MP3 player that doesn't support the amazon music app you need to buy the tracks on amazon. I think they're usually $1.99 each. Albums usually have a bit of a discount if you buy the whole thing.
If you buy tracks/an album - you can either download the mp3s from the site, or using the music app. You'll then find the mp3s in the folder that the app is set up to download them to. You can copy and paste those mp3s on any device that supports mp3 playback and play them.
My recommendation is to get a kindle fire 7 (it's an older model, so is cheaper, but you can get a newer one if you don't mind paying $30 more), and a good sized SD card. Then load the amazon music app on there and download songs for offline use with your subscription. https://www.amazon.com/Amazon-Fire-7-Tablet/dp/B01GEW27DA/ref=sxin_0_ac_d_rm?ac_md=0-0-a2luZGxlIGZpcmU%3D-ac_d_rm&keywords=kindle+fire&pd_rd_i=B01GEW27DA&pd_rd_r=78c139a5-1d5e-48fb-83b2-921a44726a0c&pd_rd_w=s0IMA&pd_rd_wg=PyCQ9&pf_rd_p=e2f20af2-9651-42af-9a45-89425d5bae34&pf_rd_r=WRD201J3Y0A0JXAHF6F3&psc=1&qid=1577644626
Or, if you have a decent phone, just install the amazon music app on there.
The cheap versions of Amazon Fire tablets seem like the sweet spot to me e.g. https://www.amazon.com/All-New-Amazon-Fire-7-Tablet/dp/B01GEW27DA
I don't think you can realistically get anything cheaper without going for something used.
apperantly only 30$. I bought it in €. just select with special offer, which means the lock screen is an advertisment, wich doesn't realy bother me personaly. The 8gb version is big enough for only summoners war, because you can use 7.6 gb of it for your own stuff, 400 mb are for the system