What kind of punishment may I be looking at for attempting to purchase alcohol as a minor with an altered ID?

First off, admit what you did. You're not going to be the first Soldier to screw up and you won't be the last. What matters is showing that you won't make a pattern of this and that you accept that you made a mistake of your own choosing. You can say PVT or SPC so-and-so convinced you to do it but you're not a robot, own up.
Second, get with your first line leaders. Explain to them you know what you did and that you want to do what it takes to fix this. Hopefully you've already made an impact on them with your work ethic. If not, you've got a fight on your hands to prove that you are worth their time.
Third, contact Trial Defense Services. They're the part of JAG that advises or defends you on adverse actions. Whether you're facing an Article 15 or a Court Martial, don't wave your rights to speak with counsel.

Good luck.

For starters, (as I understand the writing of the Articles) you violated Article 134 in the following sections: False or unauthorized pass offenses (Maximum punishment: (1) Possessing or using with intent to defraud or deceive, or making, altering, counterfeiting, tampering with, or selling. Dishonorable discharge, forfeiture of all pay and allowances, and confinement for 3 years. (2) All other cases. Bad-conduct discharge, forfeiture of all pay and allowances, and confinement for 6 months. ; False pretenses, obtaining services under (maximum punishment: Of a value of $500.00 or less. Bad-conduct discharge, forfeiture of all pay and allowances, and confinement for 6 months.

And that is if your command wishes to push for Court Martial. Otherwise, you could face the Article 15 process which is Summary, Company and Field Grade.

Maximum Punishments In Article 15s:

Summarized: Restriction 14 days, Extra Duties 14 Days, Oral Reprimand or admonition, or any combination
Company: Restriction 14 days, Extra Duty 14 days, Pay forfeiture 7 days; Reduction of 1 grade (E4 and below)
Field Grade: Restriction 60 days, Extra duty 45 days, Pay forfeiture Half month pay for 2 months, Reduction of 1 or more grades (E4 and below)

But, I'm not a lawyer so I have no idea what you would face nor what charges. I searched and found the most applicable Articles in the Manual of Courts Martial based on what you said. You could very well face different charges and face different punishments if it went to Court Martial.

When you swore your OATH you also swore to obey and uphold the UCMJ. You even had to learn the UCMJ for future questioning by your superiors, and while you're assigned 'watch duties'. It makes absolutely NO sense for you to "break any rules", let alone the UCMJ. If you get discharged with anything less than an Honorable Discharge, you will suffer long term damage when you are a civilian again. It's never worth the gamble.