I understand some weapons can push and some can put an opponent prone.

I am not sure how that affects me.    

My opponent has the normal 30' speed.   I am able to push him back 5 or 10 feet.   Does the different length actually matter?  What plus/advantage/etc. do I get for pushing him back 5 feet?

In a different fight I get my opponent prone.  I know they use 1/2 movement speed to get upright.  How does that affect me?

If an opponent can move 30 feet, does it matter if they move the distance to cover what they were pushed?  Or to get upright?

It's tactics. If you're next to a hazard, you can push an enemy into it. Also, you have advantage on attacks against a prone target (if they're within 5 feet of you) Pushing an enemy can also be useful to basically disengage while still attacking. Additionally, if you push and prone an enemy and run away, they have to dash to catch you, allowing you to attack without them being able to you.

It's not just handy to push them so you can walk away without an opportunity attack, but it also allows you to move enemies away from allies who are currently engaged so they can walk away. In my group it's often a front-liner knocking an enemy away from a squishy and then stepping up to engage it.

You can also use it to push someone behind a door and then close it, move enemies closer together to be hit by area spells, knock someone off a cliff, etc.

The benefit of prone is often the advantage it gives melee attacks. Be aware though that it means ranged attacks are at disadvantage, so it can be problematic if you have ranged allies. In those cases at least it makes it harder for the enemy to move far enough to engage those ranged allies.

Thank for the answers.  So if I am in an open field and i push them, I get no benefit from that result?

Same open field, If I have them prone, then they can get up and still swing at me so I get no advantage to that either?

If my weapon has sap/vex, then I do get a benefit, as one of us has the advantage/disadvantage result when rolling next?

If you attack the prone target before they get up, you have advantage.

Quote from Character77006 >>

Thank for the answers.  So if I am in an open field and i push them, I get no benefit from that result?

Same open field, If I have them prone, then they can get up and still swing at me so I get no advantage to that either?

If my weapon has sap/vex, then I do get a benefit, as one of us has the advantage/disadvantage result when rolling next?

 

Some thoughts on Pushing with the Push Mastery:

 If you're in an open field, and you want to get some distance from the Foe, if you Push them, and there are no other hazardous conditions or other people on the field to deal with, the primary benefit is that you might have pushed the Foe out of range of being able to attack you, allowing you to move away without recieving an Opportunity Attack (or, if you have a ranged Attack option that you consider superior that you can still use before your Turn Ends, you can swap to that  without incurring Disadvantage)

And if you Push the Foe into another character's square, and they wind up still sharing that square at the end of your Turn, they both fall Prone.

Some thoughts on knocking Prone with the Topple Mastery:

If you're in an open field, they're 5 feet from you, and you knock your Foe Prone,  you (and your friends within 5 feet) get Advantage on their attacks on that foe until the foe gets up again.  Anyone not within 5 feet of that Foe gets disadvantage to strike them. This can be very useful if you have multiple attacks, or a Bonus Action attack you can use on this turn. And if you want to run away from the Prone foe,  the foe can Opportunity Attack you, but he does so at Disadvantage, And under most circumstances, he'll have to burn half his move on his next Turn to stand up.