JetPens has good guides:

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.

Hey, thanks.

I have a Pilot Metropolitan and it dries pretty fast.

The best one I know in this regard is the Platinum #3776 Century, mentioned above. It has a special sealing mechanism so that it can go for months without drying as long as you close the cap. On Amazon you can find Japanese sellers that sell it for around €60/€70. That probably doesn't quite fit "not very costly" in absolute terms, although it's actually quite a bargain for a pen with a gold nib (and a good one, IMO!) that would cost twice as much at a shop, and can last for many years.

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.

Platinum 3776 are good and designed for this use case - the inner cap is supposed to keep inks from drying out even with long periods of no usage. If you buy a restored Parker 51, they're nearly indestructible. Just dip it in a little water to get it flowing again.