Through AutoPlaylists you can accomplish a lot. You have Criteria like Rating, Last Played and Playcount to help build AutoPlaylists and you can reference other AutoPlaylists as well. Auto-DJ can then be used to play such AutoPlaylists.

The process could be easier with more Criteria/Conditions as well as AND and OR in the same AutoPlaylist, but a bit of creative work can get good Playlists.

I always run in shuffle mode and notice when I add a new 'song' to my folder where I run from, and refresh the new song is listed and played # is set to zero.
In spite of that I so not understand it still plays songs that are played over 100 times, and it can take days for the new song is played.
I also noticed it still picks songs that were already played today.
I have also rated the songs, but the randomizer seems to ignore that.

I would like to have a weighed shuffle play rating where especially songs that were not played today today are picked with a higher preference.
I would also like to that this weighed shuffle play would add more weight to songs that have a higher rating.

on start of the day all songs should get a weighed shuffle play rating of 5
Based on the set rating those songs should get additional points added to their 'weighed shuffle play rating'
each time a song is played it deducts 4 points from that song's 'weighed shuffle play rating'

So technically the shuffle randomizer could work like this;
[*]for every first song work as you normally would
[*]for every second song, select a song with a that has a weighed rating above 4
[*]for every third song, select a song with a that has a weighed rating above 10

That means a song that is rated with 5 full stars gets 10 points and 5 added for not being played and start the day with 15.
a song that has no rating but hasn't been played gets 5 points.

That way popular songs are played more frequent, and there is less change some songs are hardly ever played.