We have an old house with no mud room. Rug and doormat right at the front and we take the shoes off immediately and put on slippers.

You can get water hogs on Amazon. We have one at each door, all varying sizes and colors. Don't let the price scare you away - you NEED these mats. Nothing will compare to trapping mud, and easily being cleaned with a hose. Winter and summer... the best.

+1 to the Waterhogs, and I think they have Mudhogs now. We shake them off and hose them down regularly.
We also take our shoes off as soon as we come in and change to house shoes/slippers depending on the season.

LL Bean waterhog mats. We have those and then a 4x6 rug over our hardwoods in the entry. and then a plastic shoe tray to the side for when the shoes are very dirty.

I don't understand why every home doesn't have a mudroom. I would love simple 5 sqft of tile where you enter that is sunken below the main floor. Stepping up onto the wood floors to enter the rest of the house so that dirt and debris was trapped on the tile once you took your shoes off.

But I cant afford to remodel my entryway into a proper mudroom right now, what can I do to the area around the door to keep dirt imprisoned? Any tips?

So far my searches have been fruitless and I'm 1 Amazon click away from ordering two new (outside and inside) doormats that claim to trap mud and dirt better than my $15 Target special.