If you can pick a good secondhand machine, that is by far the best way to go IMO.
Not only do you save on the cost of a new machine, but a secondhand purchase will usually come with heap of accesories and tools that a new won't. Do not underestimate the cost those accesories can add to the price of a machine.
Generally I find the best way to get hold of good secondhand machines is via model engineering clubs. Members sometimes upgrade, or people pass away and their workshop equipment is auctioned off or sold onto interested members.
If sourcing a used machine is a problem, then have a look at the Chinese lathes. The range of machines produced by SIEG offer exceptional value for money, and are more than accurate enough for anything you want to make for a model submarine. They tend to come with with lots of features as standard, and the accessories are quite inexpensive.http://www.siegind.com/products.php?sid=1
the C1 or C2/3 is quite sufficient for model submarine construction.
Here in the UK we have companies like Warco and Axminster importing these machines. In the U.S, outfits like Harbor freight import the SIEG machines, there may be others.
With a machine like this, you may want to take it apart on purchase and thoroughly clean it and re-lubricate all the parts. Straight from the factory these machines have been known to contain bits of swarf etc. So it's worth giving it a thorough clean and inspection before use.