Your recommendations for cost-effective and musical sounding headphones?

By audiophile standards $700 is not much. I really like Grado RS-1. Grado 225e are 'poor man's' RS-1 - very good.

It seems that Grado, Sennheiser, AKG, Audio Technica and Beyerdynamic are
most often cited.

I listened to my old "dreadnaught" Genesis' A Trick Of The Tail remastered through my recently acquired 225e phones today and, even though I've listened hundreds of times to this recording since it came out in 1976, I heard Hackett's guitar details as never before, plus Collins' melodic percussives. Quite the musical revelation. I've got about a hundred hours of continuous playtime on these by now and they continue to improve.

Yeah, this classic Grado sound is very appealing. But I don't use Grado cartridge with my turntable, need something more neutral.

I have Yamaha HPH-200WH that for some strange reason cost only $59.99 white at Amazon.  Black version is $95 (still a bargain).  It has strong tight bass, clear highs and good imaging.  I also have AKG K271 MKII and used to gave HD-580 (same drivers as HD-600).  Both sounded cold and lifeless in comparison to Yamaha.  It is "on the ear" open air design. They need a week of loud playing for midrange to fully open.  Sound is warm and very musical.  I drive them with Oppo HA-2 (USB to MacMini).