I have rented with three different offsite companies, the last time with Gold Mobility, and they were by far the best of the three in my experience. I will absolutely rent from them again. They are also highly recommended by other posters on here.
The only thing I leave on the ECV is a waterproof crib sheet that I have that I cover the seat with. Everything else comes with me when I park the ECV. Which means I bring a small backpack with me into the park. When I am riding the ECV it fits nicely sitting in the front basket. That also means I can keep an eye on it vs e.g. it being behind me where I can't see it. One of the security features of the bag I have is one of the backpack straps can be securely strapped to something, and I loop it to the ECV, usually just through one of the holes of the basket -- that way is something were to try to grab and run, they would not get anywhere with it.
The backpack I have is this one by Pacsafe:
https://int.pacsafe.com/products/venturesafe-15l-gii-anti-theft-daypack:
Pacsafe VentureSafe 15L GII Anti-Theft Daypack. I don't know if they make this specific model anymore for the US/Canadian market, however it is still available through some retailers, eg
Amazon and others. We have had ours since 2013 and LOVE it. We deliberately brought Pacsafe for the security features, plus it was the right size. We use it as a park bag for WDW trips, and as our day bag for other trips when we need something larger than a purse, e.g. for
Disney Cruise excursions, trips to the zoo. It has served us well and when it eventually dies we will replace it with another Pacsafe. On the US/Canada Pacsafe site it looks like this is probably the new version of the bag:
https://pacsafe.com/products/venturesafe-15l-g3-anti-theft-daypack
Now, if you don't care about the various security features, you can get a similar size backpack for much less. Note that the size of the one I use is probably a good size -- too much larger and you will have issues fitting it into the basket. You can go a bit larger though -- I can fit mine plus our refillable mugs into the basket, so it doesn't take the entire space.