If you already started working, file your tax return reporting 1099 income and pay taxes. That's the best way. If you don't file return, IRS will send you notice to pay taxes you owed. The employer is supposed to issue 1099 MISC payment of $600 or over to you and IRS gets a copy of it.

If you have not started working you have time to think. Difference between receiving 1099-Misc(independent contractor) and W-2 is, 1099 means you're working for yourself and you are responsible for paying your FICA (social security and medicare) taxes. W-2 means you're working for your employer who will take care of your FICA taxes.

You cannot work for anyone on F1 without CPT or OPT. As you're on F1 you're not subject to FICA taxes. (but if you're not on CPT or OPT just file 1040 and pay FICA taxes, don't make it complicated to IRS). On OPT you can work on 1099-Misc. I don't know about CPT. IRS does not care about your status as long as you file and pay your taxes. It's USCIS you have to worry about.

This is based on my knowledge on tax, I'm not expert on legal stuff. Please use your own judgement.