You original question completely left out the prop from the equation... you can't do that, you must take it into consideration before you ask the question. The prop plays a very important role in how many amps you will pull with a particular voltage on your selected motor. In fact, the first thing I'll try to select is what size prop I'd like to use on the selected motor/engine. The following are what I use to consider parts in an electric motored plane.
So I first try to select which diameter prop I want first based off the wingspan of the airplane I intend to use it on. On a monoplane ( single wing ) I usually shoot for about 25% of the wingspan for the diameter of the prop I'm going to select ( for a 2 blade prop ). This is just a rule of thumb type of "rule" and other things come into play such as if this is a racer.... I'll go with a smaller diameter prop but with a bigger pitch so I can get more speed... So this is just a number to start with so I can go ahead and select the rest of the parts I'm looking at getting.
Next you need to select which motor will deliver the required or wanted power ( watts ) for the type of flying the plane is intended for. Instead of me just repeating what is posted "everywhere" on this subject... Here is a webpage that covers the basics of that info alread...
Determine a Model’s Power Requirements
Now... You already have the motor and since you didn't tell us which plane or it's wingspan... I'll just use the specs of the motor to move on with which props are recommended which are based on 2 blade props. Here the lowest recommended voltage they list is matched to the highest diameter prop they list... and visa versa... the highest voltage is matched to the smallest diameter prop. If you are going to run a 4s battery ( 14.8v ) the biggest prop you'd select at most is a 14x10 prop... on 5s ( 18.5v ) the biggest prop would be the 12x8 prop. Trying to select a larger prop than these ( or one with more blades but are the same diameter ) will result in you pulling too many amps ( unless you are very careful with the throttle ) and burning up the motor.
Next... once you have found out which motor, prop and what voltage you are going to use... you need to see how many amps that combination is going to pull at max. When you know the max amps, you can select an ESC that can supply at least that many amps... many of us will select an ESC just over the size needed for some extra headroom so we don't risk burning out the ESC. When you know the voltage you will need for the selected motor/prop combination.... You can then also select the battery size/capacity ( mah ) you need.
The capacity of the battery ( rated in mah ) along with the C value will give you the maximum amount of amperage the battery can provide. The formula is simple.... (mah)/1000 x C rating. Tony actually misfigured the amount of amps your battery can provide... it can actually provide up to 225 amps max.
Having this value, the amps, more than what your motor/prop combination will pull... WILL NOT cause you to burn out the motor... The battery will only supply the amount of power that is requested of it... the battery can limit the amount of power you receive by being too small... but it can't push more amps than is asked of it.
The E-Flight 46BL motor is capable of handing 41-50a of continuous current with a 55a max burst current. Using 5S batteries and a 12x8 APCe prop on it... will pull at a max of 55a on v2 of the APCe prop ( or 58a on v1 of the APCe prop which is probably no longer available for purchase new these days ). The approx max for this combo is around 10,200rpm, 3060g ( 6.74 lbs ) of thrust, 124km/h ( 77mph ) vpitch and 722w of output watts of power.
You wouldn't want to run WOT ( wide open throttle ) with this combination for long but with good throttle management... this combination should work fine as long as they are a good fit for the plane itself. Of course the question that remains all deal with which plane you plan on using this combination on and if this is enough or too much power for it.
As for the question about your 3 blade prop... we have no info on it to base anything on. If you don't know the diameter and pitch or even the brand... who is to say if it will be a good fit or not. In general we can say that being a prop for nitro/gas it will pull more amps than an equivalant electric prop. I'm with Tony on multi blade props since they aren't as efficient... I don't recommend them and I certainly wouldn't recommend using one that you know absolutely nothing about. You should be able to find out at least a little about it.. look at it, they probably printed/molded the specs for it on the hub or somewhere and then at least you have a bit of info you can make a semi-educated guess from. Without that info... it should be relegated to the hanger only for show and not used or you risk either burning up something or possibly not having enough power to fly with.