A lot of players tends to train on weak animals with weapons or tools that do low damage, however by doing so you will lose out on gaining weapon skill so it's rather a trade off for playing it safe.
The Best best strategy to gain good weapon and fight skill is to find zones which has a high count of spawn with the desired animal type and keep training on them with your weapon and left hand empty of any weapon or shield. The goblin spawn point is a good idea for example.
Another thing to keep in mind is that you can gain skill from a certain animal up to a certain skill level, from that one you get diminished returns, that is training will start to get slower and slower. The skill level seems to vary a bit but is generally a range of -5 (skill levels under the animals skill level) to about +10 ~ 15 above it.
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