I'm Denise and my interest is in portable gear. What I have is a few years old, and has served me well. I'm currently using HiFiMan 601 and Grado G10 IEMs.
 
It's time to upgrade, and I'm looking forward to learning about new gear here.

What is your budget?

These IEM reviews might help: http://www.head-fi.org/t/478568/multi-iem-review-333-iems-compared-ubsound-fighter-added-02-21-15-p-1039

I'd like to stay under $500 for a source. Not a high end, obviously, but I'd like to step up from what I have.

I'd like some good cans, probably also in the $500 range, maybe more.

Probably a headphone amp.

So not a big budget, but I retired a few years ago and it's what I can do, for now. Obviously I could save and wait a bit.

For your source, you could upgrade to a Fiio X5. It has many good reviews and it is a step up from your 601. It also has 2 micro SD card slots, so more than enough memory. The amplification in the X5 should be good enough for any portable cans you buy. Actually, many $300+ DAPs should be able to drive almost all portable cans with ease, so an external amp for portable use with such a good DAP doesn't seem necessary to me.
 
For the headphones themselves I can't be of much help. My own portable cans are the Beyerdynamic t51p and the B&W P5 S2. I really like the t51p, but these are on-ears and therefore lack soundstage and sub-bass. For me the portability was an important factor.

^^

What he said. The X5 would be an excellent choice. Then put your money toward heaphones. Maybe get yourself a pair for home and a pair for on the go

Innerfidelity's wall of fame lists are a great place to look for ideas: http://www.innerfidelity.com/content/innerfidelitys-wall-fame