Ours had pea gravel around it when we moved it.....huge hassle with the mower/weedwhacker.....i dug it all out and put mulch in and then planted some hosta......no word on how long the hostas will make it as they've only been there about 4 weeks...
What is your location? For Texas I'd put 1' or 18" paver in traffic areas, with dwarf mondo grass or thyme in between unless abutted totally. Then I'd add giant liriope on 24" spacing around the non-traffic areas. At some point I'd build an attractive bed with other small plants, some evergreen and some color, depending on climate.
It is more important to keep nutgrass and other invasive weeds from growing in that space. They can come up through the bottom and damage your liner. I put a sand base and bricks around the base of my pool.
Nutgrass! Nasty stuff, the nut is about 8" to 12" below ground and pulling the weed won't kill the nut which keeps putting up new plants. Round up works to kill the nut, eventually. I think there is another product specifically for nut grass but I cannot recall the name.
japanese skypencil hollys---I reconsidered this post overnight and wanted to modify... I think I would put some small shrubs like the afroementioned hollys in containers around the base of the pool. There would be no worries about root infiltration into your pool base and they could be easily move for whatever reason you would need to move them.