Should I err on the side of too many minerals, or too much gas?

Short answer: Minerals.

Minerals build production facilities and expansions, so if you ever have too many minerals, you can build more production facilities to facilitate more units to consume your wealth. Also most units require more minerals than gas.

Gas however is more of a "rare" resource, you will often find yourself bottle necked by gas when it comes into the mid to late part of the game. In general, you need to plan ahead on your strategy. If you want a gas heavy army (such as early void rays), then start building up gas early and have the resourcing to handle a large flow of gas. If you want a more mineral heavy army (like mass marines or zerglings), or you want more aggressive expanding (popular with zerg) then go more mineral heavy.

Spanishwa is a pro-level player who gives a good example of switching focus between minerals and gas. He starts the game by going mineral intensive, so he can mass drones and hatcheries, then switches to heavy gas later when his army demands it. He also has the minerals for static defense as necessary. He shifts his focus based on what his opponent does, and as his army composition shifts, so does his resourcing.

Recent example game (I'm trying to find a better example of this, but this is an interesting example of how he can mass a ton of spine crawlers to defend an expansion at a moments notice)

If you talk/watch to pro-gamers, you'll find that this is not a decision that is made as part of the game. The closest they get to this decision is whether or not to build one or two refineries early in the game or how soon they need to get their gas running on expansions. The logic behind these two decisions has to do with what units they want to build. Overall, the resources at each base are fairly balanced. Once you're past the first few minutes after you get an expansion running, your gas should be saturated as well unless you absolutely need 0 gas for your build (which is unlikely since an all minerals build is easily countered).

If you plan on building Tier 2+ units soon, you'll typically need more gas. This will cause you to take an early geyser or grab the gas when you expand. Otherwise, it makes more sense from a financial perspective to keep the workers that would otherwise have built/mined the refinery on minerals to get those additional 40 minerals per second apiece (especially if you're going for an early expansion). This isn't a decision made based on "what should I stockpile more", it's a decision about what makes sense economically.

As you've noted, even pro-gamers are unbalanced in what they have saved up. Most of the time, this isn't because they've decided to stockpile one resource (although this is occasionally the case in the early game because they're saving for a timing push or an early expo). In fact, the contrary is usually true: The resource they'd prefer to have stockpiled is the one they don't have. Why? Because the most effective players spend resources as soon as they get them.

Any unspent resource is not contributing to your army, gathering, or technology improvements. In terms of helping you win the game, unspent resources serve as much benefit as an IOU. So, as you get enough minerals or gas to do whatever you need to do next, you spend it immediately. If you follow this exactly, you'll never be above a few hundred units of the resource you need most, and it will appear as if you are stockpiling the other resource (since you need it less often).