While the companions can sometimes be a nuisance, there's no doubt that they do have many uses - especially for solo players!
Here are my tips for getting the most out of your companion (with the least headaches!)
1 - Never give them wood to carry unless you're harvesting it for fuel. If you did end up giving them high-tier or rare wood and it goes missing, check your fires. That's where it went.
2 - As soon as you have access to "charm of the leader," equip it. It raises your companion's health and damage, upping the chances they'll save you if you get KO'ed in a fight.
3 - Your companion levels up with you, so you don't need to create high-level gear to to equip them with. Since they've been known to disappear at times, you don't want to do that anyway. Leave them with their clothes and gear you got them with. The only exceptions are a level 320+ axepick and knife. Equip the axepick when resource gathering and they will gather things they find, too. Equip the knife in battles. It's easily the highest-damage melee weapon in the game.
4 - Never allow your companion to wield any tools or weapons while trying to peacefully complete the first hunt realms, or in any tier 3 swamp realm where there are likely to be grendels. They will attack, causing you to miss the peaceful completion option of those missions, or causing you to have to accidentally kill a grendel (noooooo!)
5 - While you don't want to give them your wood to carry, DO give them anything else that is heavy and also expendable, especially if you're encumbered! Stones, gems, and ores weigh a lot, they do not have a carry limit, so you can use them to take the heaviest parts of your haul to maximize resource-gathering within realms. Just make sure you hang on to that wood, and anything ultrarare/irreplacable!
6 - Tired of having too many tools and not enough slots? Give the tools you use in realms the least but still sometimes need (for me, these are the sickle and the spyglass!) to your companion. Swap them out when you need them, keeping your hotbar nice and neat without a lot of excess tools in your inventory.