I am not sure how long you're going but my (US) experience is that if you're going more than 2-3 weeks, you're basically paying for the car seat. And when renting you often don't get great seats (we had a very cheap Evenflo seat once with a 4 day rental). So even though it's a pain, I have travel bags, we check the seats and I bring them. I don't want to waste US$150-200 on rent (car rental companies charge about $8-10 a day). You may want to keep this in mind.
It may be cheaper to buy a good basic car seat on arrival (and/or ask family to buy it for you).