Buy one from a dealer, but I seems you have a lot more problems. Remove gas cap and in an open area blow back the gas line from NEW filter. Blow Carb line back to pump. Be sure the shutoff solenoid is operating and staying open with key on.
Check Float bowl for fuel. Remove Needle. Fuel should pour out when cranking.
I'm going to estimate that approximately 80 to 90% of fuel pumps that are replaced we're never bad at the first place. It's one of those people throwing Parts at the problem and it rarely fixes the problem...at least not on the first time or two.
A pulsator fuel pump is very easy to check. If it's leaking fuel or oil everywhere or especially out of its little usually brass screen bleed hole then it's obviously bad but other than that all you have to do is make sure fuel is getting to the inlet port and take off the fuel line at the carburetor and crank the engine over or better yet pour a little bit of fuel in the car throat and let it run for five or six seconds and see if gas goes pulse pulse pulse out of the fuel line.
If it doesn't, it's still not exactly time to replace the fuel pump until you make sure that the lines aren't cracked and for the big one make sure I mean absolutely sure it has fuel on the inlet line. Even if you have to run an external tank for a couple of minutes that you see fuel flowing freely to the inlet, do so before you condemn a fuel pump.
Then, if you need to buy one order one on eBay or Amazon for under $9. They are all over the place. Briggs & Stratton round plastic style is the most common and of course there are three port. There's also a four port on the market and some metal ones but regardless all those round three ports will work and there's no reason to pay more for a Briggs & Stratton and especially no reason to pay more for a Briggs & Stratton that John Deere puts in their yellow and green plastic baggie and raises the price 40% or is that 60% now.
Knowing what you're buying and knowing what you need is the key to this game. Buying by brand etc is typically wasteful and you're usually not getting what you pay for.