I have experience with all of those, and have played with all of them together at one point or another.
Stability is not a huge issue for most Stardew mods. In my experience, I have only had crashes if the mod was for a different game version, or if it was a mod that added in a new machine and it was missing another base mod to function. Anything that expands the world should be fine as long as you have added any mods they require to work.
Any mod that expands the minecarts has the potential to get a bit weird, but Integrated Minecarts is the best of them that I have used, so you should be okay.
Stardew Valley Expanded, while a popular mod, may not be compatible with other mods as there are several mod authors who would prefer to not work with that author or anything they make. Iirc, this is due to them having harassed other mod authors they accused of stealing concepts, as well as a lot of people not liking the fact that the author added in weird dialogue about sexual assault for one of the characters and had no warning of way to avoid it. I personally don't use it for these reasons, but I don't personally think there's anything wrong with using it, just be aware that it will have more compatibility issues than most others.
Removing almost any mod mid game will cause issues of varying degrees, since it will cause the game to try to load assets in a save that won't exist. Most mods will have a recommendation of whether or not you need a new game in order to start using a mod, and a good rule of thumb is: if it needs a new game to start, it will need a new game to remove it as well.
I highly recommend getting the Mod Updater, which you can find the link to on smapi.io, which is where I get most of my mods. They tell you if a mod is working, broken, or if you can use another mod in place of one that is broken. Also, the Mod Updater lets you make sure you get any fixes to mods, which helps cut down on a lot of issues.
If you do run into any bugs with a mod, I do recommend checking the mod page and seeing if there is a fix. Hobby mod authors are almost always releasing fixes or unofficial updates, so chances are someone may have solved the issue, of found out how you can solve it for yourself.
Finally (sorry this is so long!), I will issue one warning that is based on my personal preference and experience, so please disregard this if you feel differently: while I like the expansion mods from time to time, any mods that add in a new area tend to make me spend much less time in the original areas of the valley. This has often led to me not feeling like I am playing Stardew, and Stardew is a game that I am usually playing because I want to play Stardew, as opposed to playing it to pass the time of passively enjoy. If you play for a similar reason, then I would stick to mods that add new stuff to the existing valley, rather than adding new areas outside of it. There are plenty of both, so you won't be limited either way. But again, that is my preference, just wanted to share because I have heard similar feelings from other modded players.
Hope this helps!