6A New homeowner looking for advice on challenging setup

https://imgur.com/a/HzgZr Here's my back yard. I tried to capture the majority of my problem areas in one image. I bought this house and I suspect it was being rented before because the yard is in terrible shape (not to mention the owners seemed to hate grass based on how much concrete there is).

The soil is really uneven, lumpy and it seems like several times the old owners just dispersed mulch in various areas to get rid of it. It even looks like, in one spot, they emptied fish tank pebbles out. I tried to rake up a majority of them.

My main questions: -in my lawns current state, can I rent one of those heavy barrel rollers to flatten it out? -do I need much prep work before planting grass in barren areas (of which there are a lot!) -how much do I need to worry about cleaning up mulch and small pebbles before planting. -Any tips on tilling large (10x10ft) areas of soil to prep for planting. -Oh, one final thing, my neighbors have some type of vine/ivy that spreads through my yard. In certain areas I can run my fingers through the grass and pull up a vine or two the circumference of maybe half a pencil. Any tips on this?

I am really looking for any and all advice. I know I need to get a few bags of Milogranite. I am determined to have a nice yard to enjoy with friends and eventually kids.