The warp yarn is most often a different, stronger type of yarn than the weft. Your weaving will only be as strong as the quality of your warp yarn. The warp holds everything together.
Some fine yarn and/or weaving suppliers have specialized stocks of weaving warp available on 'cones.'
The yarn that is best for this type of weaving is a strong cotton yarn of a weight between 'sport' and 'worsted.' The cotton can be mercerized or be natural. Wool warp is also used, but finding one of the proper strength and durability can be a challenge.