Fountain pen technology has come a long way! I've never had any problems with leaky pens. You can get some very nice fountain pens for around $20 these days.
One of my favorite fountain pens is the Pilot Varsity - it’s a disposable fountain pen. Lots of ink combined with one of the best nibs out there, no matter the price. There’s an entire set of users out there dedicated to figuring out ways to refill these so they can re-use the nib. I haven’t had a single one leak on me, either.
Yeah, in my foreys into fountain pens they were one that "felt good" to write with. Some had tips which snagged when you end up "pushing" as a lefty, but the Varsity was smooth.
If you want to feel fancier, the Pilot Metropolitan uses the same nib (in fact, since they don't sell replacements, you end up buying a pack of Varsities if you need to replace the nib).
They go for around $2 each.