Nakka has a great spreadsheet to generate the gores for an ellipsoid parachute. Fruity Chutes has a good online calculator you can use to size the chute to your recovered weight and desired descent rate. A Cd of 1.5 for an ellipsoid is a good number to use.
I would recommend using 1.1 oz (or 30 denier aka 30D) calendared ripstop nylon for a chute. You can get that from several sources online (Ripstop by the Roll has reasonable prices per yard but there are others out there). I've used medium-weight (tex 40) sewing thread with good results but tend to use Tex 70 (aka Type E) thread as my standard to give a little extra robustness to the stitching. I use 8-strand 200 lb braided Spectra fishing line for my suspension lines as it packs small but Dacron kite line or even braided nylon would work Avoid any twisted cord (use braided).
When you design your chute, I recommend a apex vent 10-20% of the skirt diameter (only 1-4% of total canopy area). The vent will greatly improve your stability under the main.
I make cutting templates from 1/8" masonite board and use a hot knife (or a filed down soldering iron tip) to cut my fabric. This seals the edges and prevents fraying while you work. I use a needle tip soldering iron to tack weld the seam margins for sewing, then roll the seam edge under in a flat-felled seam for extra strength. I would recommend basting a 1/4"-3/8" twill tape in your apex vent hem before you roll it and sew it down. You won't need a tape rolled in the skirt hem.
Feel free to DM with questions on your project. I'm happy to advise on construction, sizing, materials, etc.
Steve