Hi Fitz,
while not one of the clothing gurus on the board, I thought I would ask the traditional set of questions. 
1) What time period?
2) What class/profession?
3) Geographic region?
Even if you posted this before in another thread, it may have gotten buried and a refresher would help. 
While not as well read or experienced as many, knit isn't authentic but worsted is. However, the pattern would probably be much more difficult to cut and wear.
Quality of linen would also probably depend on social standing in your chosen time period, but should be white.
I cannot answer for weight on the linen, our shirts tend to be on the light side. I suppose it would all depend on the climate you are playing in and when you plan on going to events.
One of our members has a very nice heavy wool doublet that he will only be able to wear in the cooler times of the year. To wear it in the summer... well heat stroke comes to mind. 
Hope this helps some.
~J