I have a multi-burner portable stove that I use for chicken wings. The amount of time it takes the oil to heat up is entirely dependent upon the BTU rating of the burner(s).
Mine takes roughly 5 minutes to come to 350°.
Tips:
Do not exceed 350°, or the oil will burn and give an off taste to the wings.
Don't use the big tall pot for chicken wings, it's a disaster waiting to happen. Go to Home Depot or Lowe's and get the shallow pans with fryer baskets. If you decide to use the big pot, there may be too much volume to quickly and evenly cook the wings. Remember the Turkey Carcass is hollow and it cooks on both the the outside and inside simultaneously. With a half pot of wings the temperature of the oil will drop quickly and the center mass will stay cold.
Keep a fire extinguisher close at hand. Obviously one that is rated for oil fires.
Keep the cookers away from crowds, away from vehicles, and away from anything flammable.
It is important to use a basket to drop the wings and take them out of the oil safely. I cook about 20-25 wings per basket.
Never fill the pan with too much oil. When the wings are dropped into the oil thy displace the volume in the pan, secondly the water content from the wings can cause the oil to violently boil. If the oil level is high in either case the oil can flow into the burner and create a violent oil fire.
When the wings start to float and they are golden brown, they are done. I prefer to never drop frozen chicken wings into the oil. Thaw them in the refrigerator overnight.
Save your brown paper grocery bags. When the wings are taken out of the oil, let them drain for a second, then dump them into the paper bag and shake to remove excess oil on the wings. A bag can be used 5 or 6 times before it will not remove surface oil on the wings.
Dump the wings from the paper bag into your warmed sauce, remove from sauce and then serve.
For wing sauce, I use straight "Franks" from the gallon jug. For medium heat, I mix 50/50 melted margarine and "Franks". I don't think a girl's soccer team would want anything much hotter.