you can take that logic even further now. Floor traders moved upstairs since the late 90s, which lead to more technically competent people getting in the industry and now those ex-floor traders who trade upstairs are losing their luster leaving the technical guys taking over the trading. So basically, if you are manually trading you're done.
If you can get the job with Chopper, that is by far the best option of all 3. Like Mav said, they are a top firm in Chicago. But forget about a nice work/life balance. You will work long hours there, and I believe the new guys hired are clerks for at least 18 months working the overnight shift as they learn (5 p.m. to 5 a.m. Sunday to Thursday). So you will have to give up your social life for the next year and a half.....but in the long run will be well worth it.
I suspect you already know which one you want to do and you're just waiting for someone to tell you you're not a fool for taking less money. You're not. Go for option 1.
Without a doubt. Your whole list is in reverse order. Take 3 (Chopper) first, then 2 (the internship), with the floor bringing up the rear. It hasn't been relevant for 10 years. Honestly, it's amazing that it's still around at all. Be prepared to really work, though -- your toughest competition won't be too worried about work/life balance, no matter where you wind up.
None. (By the way, it has to be options trading... because really nothing else is traded in the pits these days. Just about any underlying, regardless of order size, is already traded electronically.)