If a Compel is the most interesting way to gain Fate Points, then how serious should it be? What kind of trouble does a character have to go through to get one? If it's too bad, they might end up having to spend that very fate point just to get out of trouble...
How serious/severe/time-consuming/resource-consuming should a compel be?
There is no set "rule" on how serious it should be. Being a narrative component to the game, the severity is also hand-wavy.
The compel should be severe enough that your players stop to think about it, maybe even give the GM—or whoever is offering the compel—an eyebrow raise, but not so severe that they pay it off without thinking.
It's an art, to be sure, and every group is different. It's going to take some time to get it "right", and that's ok. For a lot of the early compels in a group it's best to discuss them, offer and counter offer, and then decide on if it's worth a compel.
A compel should be severe enough for the compelling player to justify the fate point expenditure, and plausible enough for the compelled player so that they may consider accepting it.
What that means depends so much on your story…
The severity of a compel depends on your game group. Compelling is a trade and if you find your players always paying to avoid your compels (or each other's) then the severity is too high.
A timid group of players new to role-playing might not want surprises in the same way a group of seasoned and gonzo players might take any compel you give them just for the fun of it.
When you give someone a Fate Point for a Compel the severity of said compel only depends on what your group can agree on. As far as Fate is concerned one of the biggest ideas is to make sure everyone can agree/have agency. as long as any compel you give has any consequence that must be dealt with the only obstacle to it being a good compel is if everyone agrees that it is a viable compel. This usually means the GM and the character being compelled, but everyone at the table should feel free to say something if they think a compel doesn't work in a certain situation/or with a certain character, so the idea is really just to establish as a group that a compel works through discussion and agreement. Another big deal in fate is that the consequence should make things interesting, this is true in a lot of things in fate so if your compel doesn't seem to interest anyone it probably shouldn't be used, but if it does, then that means it is a good compel
with my group, compels range widely in terms of actual seriousness/severity, and the time they take to resolve. in one instance, a character I was playing got stuck in a time portal, this was not resolved for at least half a dozen sessions or more and I had to use a different character. The key to why this was OK was that I bought in from the start on this (it actually happened to be a self compel, not that I wouldn't have gone with it if it had been another person's idea), but other times we have had compels that have resolved by the end of the current session or even earlier. Not every compel needs to make a sweeping change to the story, some of them only need to be a mild inconvenience that trips you up enough for the bad guy to get away (at least briefly) or a problem that can be reasonably solved with some investment of time and effort.
As far as resource consumption no compel should automatically cost any resources(but the recipient of a compel can still accept a compel that just gives them a consequence if everyone including them is fine with it) if by those you mean fate points and/or consequences sometimes a compel will cost a lot, and sometimes it will cost very little. If you want a guideline for it they should not average out to costing more than a single fate point or consequence (at least until you get more comfortable with how it works for you), though your group may find it more fun if they range in severity and cost.
In the end, your group will have to hash out how it works for them/you through play, but this should not be too hard to do, and you should find that it will vary at least on occasion.
It's got to make the story better. That's the whole reason for passing the Fate Points around in the first place - to encourage more people to contribute to a better story.
