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I've only just started but I can't find this info online yet.
This question / problem has been solved by advowsonimage
The definitive answer is to consult Jarulf's Guide, which will tell you this and much much more. All axes are two-handed (3.1, page 17). All bows are two-handed (3.1, page 18). The Maul is two-handed, except when wielded by a Hellfire Barbarian (3.1, page 18). All staves are two-handed. The Two-Handed Sword (an actual item base type) and Great Sword are two-handed. Lesser swords are one-handed.

The quick answer is that if you try to equip a two-handed item, the game won't let you have the other hand busy. If the other hand is free, it will get a dimmed copy of your two-handed item to show that you are now using both hands. If your other hand is busy, you can't switch from a one-handed item to the two-handed item.
The size of it is a good indicator.
Yes, item size in your pack is a good approximation. Generally, a weapon that is 2 wide will be a 2-handed weapon, while an item that is 1 wide will be a 1-handed weapon, but there are exceptions to that. The Grandfather (unique Great Sword) has as one of its unique properties that it is a one-handed weapon, despite being based on an item type that is normally two-handed. In Hellfire, Shirotachi (also a unique Great Sword, but present only in Hellfire) is one-handed.

All shields are 2 wide, and no shields are 2-handed shields.