On one of your posts you told folks where you lived. If you go to your profile page and add the info, it would show in the upper right corner of all your posts so people could give you better answers based on your zone and climate.
Would it be possible to walk across the street and take a photo showing the entire front yard?
I have cut down plenty of trees either by myself or with only one person to help. Your two trees look bad and at least one of them has potential to cause damage to your house; the trees are small enough that you should be able to cut them down without professional help.
Once the trees are removed you can get to work on the lawn, soil preparation, re-planting or re-sodding. After you get the lawn looking good you can step back and look again at the whole picture and decide where in your landscape a tree might look best. There are plenty of smaller trees that would provide visual interest; flowers and a nice scent would be a plus.
