I don’t personally like pebbles much . . . they’re so slippery, and I never feel very secure walking across them. On a slope I don’t think they’d be much better than the mulch and might not be too safe. Gravel would be better, but it would need to be small, and definitely not round.
Here in Austin we use decomposed granite. It’s very small stone particles and dust, not round but somewhat jagged. It packs well because the stone particles "lock" together under a little pressure. The surface stands up to rain running across it; it doesn’t wash on a gentle slope if it’s well-packed.
I did a quick Google to see if it’s available in your area; apparently some of the contractors have it, but I don’t know if it’s as easy to get there as it is for us. If you can’t find it, look at a stoneyard or building supply house for "crusher run" or "crusher dust". Those are other kinds of crushed stone that would also pack. The color will obviously depend on the kind of stone it’s made from.
As a do-it-yourself project a decomposed granite or crushed stone path is very easy. We used the green metal edging available at any Home Depot for the borders, and basically just dumped the granite inside and raked and tamped it. For one area we’re using for outdoor dining, I rented a compactor for a few hours to pack it well and make it hard. I would recommend that you do that if your slopes are more than 5-10 degrees.