The chainmaille mantle does not need to be part of a coif. It can (and is) worn separately as well. It is also another good candidate for first project since its even smaller than the coif - standing at about 1800-2000 links its something that you can do in about a day or two by yourself - you won't have to shanghai your family for the job.
You can find 3 uses for it, depending on your local larp rules.
1 Since it only covers the neck and shoulders often it will not always be counted as armour. Some larps have rules about coverage. In those cases it will be an addition to your costume.
2 If it can count as separate armor piece - by all means use it as such.
3 Or you can use it as a supplement to your other armour. Case in point here is a photo of bulgarian reenactors where the guy with the breastplate is using a mantle not unlike the one above to protect his lower neck and shoulders.
You'll need basic tools, about one, one and a half kilograms of links. We will basically do the same thing shown in the mantle piece guide for coif, except this time we have 4 rows.
Here are the strips in almost finished state.
And finally the finished mantle piece.
You might consider adding a couple of laces to your garment to keep it in place, especially if you are running around a lot. Which you will be if you are a fighter...
Again some of the photos are taken from the internet and belong to their respective owners.