What to upgrade first?

If you go with speakers first, do not choose them because they sound good connected to your current receiver. Once you upgrade the amp, you may be disapointed with how the speakers sound. A better pair of speakers will be more detailed and revealing, and may sound bright and thin connected to poor electronics. So if you want to do speakers first, have a rough idea what kind of amp you want to get later, and use it at the dealer to audition speakers. Vice Vera for a new amp connected to your old speakers. A better amp will make your old speakers sound better, so that may be a better starting point, but still audition the amp on some other better speakers at the dealer.

For around $500 to $600, the B&W DM602 S2 are a good choice. An NAD integrated amp is a good choice in the $400 to $500 range.

All of the advice and makes/models recommended here are excellent. I would especially heed Sugarbrie in terms of listening to either speaker or amp w/future upgrade potential if you buy from traditional storefront. OTOH, Jeff's advice about buying good name used gear here or ebay and then being able to re-sell is a sound approach and doesn't require delayed gratification.

THANKS to everyone, your responses were insightful and educational. My thinking tody is to upgrade the electronics first via an integrated amp, which means I will need to get an FM tuner at some point. After settling in with the amp
I can, as suggested, listen to lots of speakers and kind of narrow the short list down. The NAD C370 2x120 seems to have all the controls and features for me now and in the future. I found an on-line seller (The Happy Medium)who quoted me $557 + UPS Ground, no sales tax. If anyone knows of a better priced source please let me know. Thanks again.

If you are looking at $557 for the NAD, consider a closeout Audiolab 8000S from Artech Electronics (if they have any left) at $549, a discontinued $1100 amp that was very highly thought of at the retail price. I'd be shocked if it wasn't a big improvement on the NAD.