LMR-400 at the minimum.
Look at the cost this way... better to spend a little more NOW to get quality coax (and 8262 is not known to be a good V/UHF coax), than to have to rip out the coax used, throw it away, and then replace it with the good stuff. Consider the "cost" of your time & effort as well, especially if you may have to "undo" and then "redo" the job.
One suggestion: As long as you're drilling a hole for coax, drill an extra one or two. Saves time in the long run, do it while you have the tools handy. Now, if you can get one at a hamfest, you could mount a "long barrel" (12 inch to 18 inch double-female SO-239) for future use, or even just put a short run of coax there (I would put a baggie and a lot of tape around the outside connector to protect it from the weather)
You may not have HF today, but you might down the road. Or have a need for another V/UHF band. etc.
Just a suggestion.