Each album has quite a distinctive sound so you can give each one a quick glance to see if you like their "era", it's possible you might like some in the era that you don't like in others but to save time...
Pre-GAME is probably the least popular era outside Japan, the rest are all a mix but I've generally seen it go like JPN > LEVEL3 > Triangle > GAME online
Pre-GAME: There's a lot of variety here since it was a long period..
https://youtu.be/XFspdThBHqM (I'd also say worth a look are songs like Electro World, I'm a big fan of Akihaba Love but that is
not a nakata song.
GAME Era ( 2008 ) - GAME :
https://youtu.be/TWSx2HaY7BU
Triangle Era (2009) - Dream Fighter:
https://youtu.be/rBX5YGPNDbs (try Edge, a fave of mine)
JPN Era (2011) - Natural ni Koishite:
https://youtu.be/edyARJq9sgM (this is a great era, you might want to look up Glitter, Spice, Nee, 575, Laser Beam...)
LEVEL3 Era (2013) - 1mm:
https://youtu.be/ihNaFCEd0Ms (my favourite era, other highly recommended mentions: Spring of Life, Spending All My Time, Hurly Burly, Handy Man, Daijobanai, Koi wa Zenkei Shisei
Current Era (2013 --) - Pick Me Up:
https://youtu.be/vhfYis6VuXY (current. You've heard Star Train, I'd try out Ijiwaru na Hello and Toumei Ningen as they are my favourites from this era)