I can get a DC 24V up to 15A power supply on ebay for 30$. If I pushed it to its limit I would possibly be able to get 360w out of my motor, I just want to make sure that either one of the surplus motors can handle this.
I understand that an AC motor might be better but I cant seem to find one at the same price range and torque capacity.
I would say that if you could find at least the AC motor unit to a household ice cream mixer (or a rotisserie spit, or some other similar slow-rotating gear-boxed shaded-pole AC induction motor meant for moving large food-based loads), you might be better off. This is simply because of the stalling issue, which I explained before.
Now for the DC motor, I am looking to make some smooth ice cream, so once it gets thick enough for the motor to stall the ice cream should technically be ready.
That's technically how all ice cream is made; its made until super-thick (which may or may not stall the motor - depending on its power and gear train strength), then the paddles pulled out and either eaten soft, or put into a freezer to solidify.
What I thought of doing to protect it would be to install a breaker that would pop at like 14 Abe mps to make sure the power supply does not overload.
This may or may not work; I know this for a fact. It will depend on how powerful the motor is, and how strong the gear train is; if the gears are metal and helical mesh, that's a potentially much stronger gear box than say one made from regular square-mesh spur gears made of plastic. But even a metal gear train is no guarantee - I recently had a smaller 24V Pittman gear motor with metal square-mesh spur/pinion gear combos break the teeth off one of the pinions due to the power of the motor. My main mistake was in not having any kind of stall protection (I was performing some manual tests on a steering mechanism on a robot platform); the motor was much more powerful than the teeth of the gears, and snapped them off easily.
If I had in place a protection method, this likely wouldn't have occurred - but the question would've been "which protection method"? Well, the fastest would've been best. Its a real possibility that a circuit breaker wouldn't have caught the stall condition fast enough. A temperature sensor (and attendant cut-out circuitry) would've been waaay too slow, too. A fast-blow fuse might've caught it, if I sized the fuse real close to the stall current (or under). A circuit monitoring the current to the motor would've likely caught it the fastest.
So you may want to re-think your over-current protection, especially with a brushed DC motor. If your protection is too slow, then you risk breaking gears, or even burning out the rotor coils (or welding the brushes to the commutator!). Ideally, electronic over-current protection is best; if you can source an adjustable current power supply with over-current protection, you could likely use its electronic protection system as a quick electronic cut-out system (provided you adjust things right!). A quick-blow fuse is the next best option, but you have to size the fuse properly; a tad too big and it might not blow before it breaks the gear train.
My other problem will to find a way to attach the shaft to the mixing blade. I want to it to be easily detachable so I can easily take it all apart to clean.
There are plenty of options available for shaft coupling. What you might do is drill a hole thru the output shaft (remember, coupled to the motor via a compliant coupling, as I mentioned before, so-as not to cause motor bearing damage), then make the shaft of the mixing blade out of a piece of hollow (or the end bored out) stainless steel (note: any part coming into contact with food will need to be stainless steel, or some other non-reactive food-safe material), with a hole thru it. Fit it over the shaft, and put a clevis pin thru both to secure it.
Now my problem is that I have no idea of the peak current of any of the Surplus motors so I don't know to what I can push it yet... I don't want to buy one of them, wait two weeks to get it to find out it wont be able to do the job
A motor doesn't need current "pushed" at it - a motor draws a specific amount of current based on load. The values that (most?) of those motors listed from "Surplus Center" seemed to indicate the running (no load) current. You can expect the loaded current to be a multiple of this, and the stall current to be much higher; but you won't know what that stall current is until you either contact the real manufacturer of the motor, or test it yourself (with a brake system of some sort).
The number you really need to worry about to know if the motor will fit your needs is the torque rating; both of the motors you listed have fairly large torque ratings (one was 38 inch-pounds, the other was 47 inch-pounds). What these numbers mean is that from the center of the shaft, out so many inches, how many pounds they could lift (if you had a lever attached to the shaft of that length) - so, one inch away from the shaft, the one motor could lift 38 pounds, the other 47 pounds; conversely, 38 inches away (or 47 for the other) from the shaft they could lift one pound. Since your paddle isn't likely to be more than 12 inches in diameter (6 inch radius), those motors will have plenty of torque - even if your paddle was double the size, they'll still have a lot of torque.
Whether that will be enough torque to mix ice cream, though - I don't know (how much torque does it take to mix such a mixture?); but it should be possible to find out from somewhere - I would imagine that somewhere there is a book on industrial food preparation that might have such information in it.
You can sometimes gauge the maximum current draw from a motor to be several times its running current, but it all depends on the motor, too. I've seen stall currents 5 times larger than running currents on some motors, but others it is even larger. You might simply contact "Surplus Center" and ask them if they know that rating for either of the motors. Its important information to know, so you can size your power supply, as well as your over-current protection system.
I would first look into seeing if you can find what the torque numbers are for mixing an ice cream mixture; once you have a rough idea of that (and note, you might find anything from inch-ounces to foot-tons and everything in-between including metric numbers - so be prepared to do some conversion math to get the numbers needed to compare for each gear motor), then you can narrow your needs down based on the size of your intended paddle, the current draw, etc. Also remember to add a bit extra current draw needed just for the mass of the system (a few percent).
Good luck.