Curt, you can do both. In the past on lengthy trips I have purchased locally, one has enough time to source chemicals and other stuff.
When on a short trip of about 2 weeks I have taken my own chemicals in powder form. Usually D76 this is the easiest way in 1 litre kits and used 1+3 to wring out the most films.
For fixer I have used Agfa Acidofix which is a powder in 1 litre packets, this is usually enough for 1 trip.
I use either water or vinegar, for stop bath.
For the last 16 years I have mixed D76 from raw chemicals for almost all of my B&W films.
On my last trip 14 weeks ago to Germany I pre-mixed D76 into plastic ziplock bags and put them into an old ID11 cardboard box. It gets only a cursory glance when packed alongside a Jobo 1520 tank and two reels.
I have thought of changing to Ilfosol for convenience but old habits die hard.
One of the problems a visitor to a country encounters is trying to find that elusive shop carrying the film and chemicals you are used to working with before you move on to the next destination. To this end I carry my own film and developers and find it a breeze to develop after the evening meal. Most of the time, especially with window shutters that are prevelant in Europe, I don't need to use a changing bag. If the weather is warm meaning sweaty hands in a changing bag, I just wait till after sunset and I'm off.
You really would be amazed at just how little you need to have. A wire coat hanger (which you carry) can be hung on a wardrobe door and after it has been bent away from the door, is a perfect hanger for film drying.
Last but not least, take enough film filing pages for the film you take with you, plus some more in case you purchase more on the road. These days it's pretty hard to source this product easily.
Mick.