From this list, I can personally vouch for the Platinum Preppy and Pilot Metropolitan. Though the Preppy is a disposable, the catridges from the non-disposable Platinum pens fit it. You could could even get an eyedropper and refill the cartridge from a bottle of ink.
https://www.jetpens.com/blog/great-beginner-fountain-pens-th...
Most of my collection is in the under $20 range, most under $2.50 and the worst I've had is the ink had dried, which took some soaking in water for a bit to get out, but this was from letting a pen sit unused for months.
I have a Pilot Metropolitan and it dries pretty fast.
I have heard that some Sailor pens also have a similar sealing mechanism, but I don't really know which. I have tried maybe a dozen fountain pens a bunch of inks, but I'm far from being an expert. However, if you go to the forums at http://www.fountainpennetwork.com/forum/ you will find real experts. You can ask for what you need and you will get answers for sure, it's an awesome community.