What would you use (or have used) for:

Linen shirts:

Linen doublets:

Gloves/Gauntlets:

Brigandines:

Tents:

Archeological samples of string (esp. linen) are difficult to come by and especialy so in quantities that would enable one to calculate a comparable manufactured weight. The most frequent figure given in archeological / museum reports is the number of string per inch or cm. The observations below are based on my experiences working with string for weaving and hand sewing.

String is usually sold by length for "small" amounts or by weight for the sorts of amounts that one might use for weaving. When buying string one will often see several numbers: first is a number such as x/y this is a measure of the thickness or weight of the plys in the string and the number of plys, another common measure is the number of yards per pound or oz. The following is an example description that one might see in a string catalogue:
Newport 16/2 Linen - Yards/lb: 2400 Yards/unit: 300 Wraps/in: 30 Tabby sett: 15 to 18 Twill sett: 20 to 24

In this example the "weight" of the plys is 16, i.e. 1 lb of this string would include 16 300 yd lengths of 1 ply. This particular string consists of 2 plys, and so there are 2400 yards of the whole string in 1lb. It is sold in 2oz cones which are 300 yds long. If you just wrap the string around a ruler so that one wrap just touches the next you will get 30 strings in the space of an inch. If you were going to weave with this string the manufacturer / store recommend setting up you loom between 15 and 24 strings per inch depending on the type of weave you will be doing and how dense you want your fabric. After finishing the fabric would probably end up between 18 and 28 strings per inch. This would put fabric made with this string on the coarser side of the fabrics used in the 15th century german embroideries.

My last linen weaving project used a string that was about 6,000 yds/lb or 40/2. I have been using the left over string off the loom for hand sewing since when I cut a project off I am left with 24x25x2 pieces of string that are about 30-36in long which is a fairly handy length for sewing. (BTW if anyone is interested in a hank of string for sewing, let me know and I'll send some to you.) My experience is that you want a string for sewing that is similar in weight to the string in your fabric. Another observation that I have made is that I much prefer working with a string that has two plys over one. It is much stronger and less prone to abrasion and breakage.

So my observations on string weights for linen (wool and silk have different weight measurements):
8/2, 8/3, etc - good strong cord suitable for warps in rugs and carpet.
10/2, 14/2 - fairly coarse string okay for hand sewing especialy for a contrasting decorative stitch
16/2, 20/2 - coarse or heavy weight fabric hand sewing
20/1, 40/2 - good for general purpose hand sewing, may be a bit slubby, but is realitvely inexpensive
60/2, 70/2, 100/3 - generally sold for lace makers, frequently a high quality, very smooth thread, that will work very well for hand sewing, will also tend to be a bit more expensive.

So hopefully somewhere in this rambling I have given you an answer that you can use. If you have further questions I'd be happy to try and answer them.