Set the pusher as high as it will go. Maybe 1 notch down, but probably not. It might seem weird the first 2 or 3 weeks but the grass will get thicker if you do that. That's about the only freebie you will find. The crab grass won't be there early Spring and hopefully the grass can get ahead of it if you keep the mower high. You want the lawn to crowd out the weeds. This can take a couple years to really get there. Train Fido to poo in a grid that covers the lawn.
A small lawn like you have could be treated for not much money. The weed and feed you connect to the hose and spray over the lawn is better than people think. Follow the instructions and keep moving with it. The spray you hire would really be the thing to do if someone will give you a one timer.
I really think all you need is for someone to throw you a bone and spray you early and then mow it right. It will do so much better for so very little.