If you have the correct FFL and have a boatload of money, you can own a machinegun.
The "Boatload of money" part is spot on but the FFL stuff is incorrect. There are basically three avenues you can take to purchase NFA items:
1) You can obtain and fill out an ATF Form 4 (2 copies) providing personal information and complete details of the item to be purchased (including serial number). The fact that the form requires a SN means that you have to actually make the purchase from a NFA dealer (Class III FFL) who will hold the item until the ATF reviews the paperwork. They supply you with the SN. You then procure two "passport" sized photos, head to the police station and have them fingerprint you and "sell" you the print cards, run a background check, and round up the "chief law enforcement officer" of you county or parish and have him sign off on your paperwork. You then submit the forms to the BATFE along with a cashiers check or Money order for ($200.00 for full auto, short barreled shotgun or rifle, or suppressor, or $5.00 for any other weapon under NFA rules). Then you sit back and wait for 90 to 180 days for the ATF to process your paper. If they find nothing to quibble about they keep one copy for their records and send back your application with a n attached tax stamp. This completed form or copies thereof must accompany the purchased item when ever it is removed from the registered address on said form 4. Very simple, very easy, people do it every day (if you read the MSM).
2) You can form a LLC corporation for the purpose of holding your gun collection. You still have to fill out the Form 4 but you can skip the photos, fingerprints, background check and chief LEO sign-off as a corporation is a "legal entity" (person) in the eyes of the law but it has no corporeal presence ans so those requirements are waived.
3) You can form a "living revocable trust" which works like the LLC corporation, and for the same reason. However it provides some benefits not found by "going corporate".
Corporations have to file with the state and produce annual reports, and other reporting requirements. Trusts, on the other hand, do not. Nearly all states allow you to form a living trust without registering it with state government, some dozen or so states do require registration but none enforce penalties for not conforming so it's more of a suggestion then a requirement.
A trust is by far the best choice if you plan on keeping a low profile (below the radar!)
There are limitations on the origin (& age) of full auto weapons available to the general public. The Firearms Owners' Protection Act of 1986 made it "unlawful for any person to transfer or possess a machine gun" unless it was manufactured and before May 19, 1986.
This limitation created a finite number of full auto weapons available for purchase and the limited supply has caused a great escalation in asking prices.
Regards,
GtG