show overall space in a picture that also includes the house

yes.. a pic would sure help us nail it ... add it in a reply ...

trust me on this.. you want NOTHING that claims to be fast growing ... as it will ... too fast.. exceed your space ...

trees simply do not stop growing at some magical height ... so fast to fill your space.. fast to exceed it ...

also.. many of the 'fast growing' trees ... are inherently weak because of such ... many are soft wooded ... so they tend to start breaking down faster than other trees ...

finally ... with trees.. we deal with tree time.. and that is usually counted in decades ... so it will be a long time.. before anything starts adding significant shade ...

without a pic.. a nice smallish tree.. with a bit of spring pizzazz .... might be a redbud ....

ken

Ok here are some pics. The tree in the foreground is what's getting cut down, so that's where the new tree would be planted.

It looks like for that position you might be after what is generally and commonly called a shade tree ... having a canopy that is decidedly overhead with some good ground clearance ...?? I agree with Ken that anything called "fast growing" probably also has too many undesirable characteristics. Most any tree is fast growing enough if one simply gives it some extra water and a little fertilizer during the growing season. Of the many characteristics trees offer, fall color might be one worth pursuing in a desirable shade tree. That leans towards red and sugar maples, male gingkgo, yellowwood and tupelo as some examples. Patented trees especially will give the best fall color displays.

If you are going to plant another tree reaching some size in time in the same spot then I would remove that small retaining wall, which is not in scale with the existing tree. Also the wall is not level anyway.

I have to agree with Ken..... my neighbors had a large tree(can’t remember the name), that sat right next to the corner of their house. Why it was planted that close, I don’t know, but it died. The city required it to be taken down. I had to have the stump ground out, because I have always been allowed to garden o the side on the house. To this day, inspite of filling the hole, it still sinks, mushrooms grow in the area and every time I dig in and around the area, it is full of roots. Tree has been gone for 6-7 years now (?)

I love the Black Tupelo, especially the Wildfire variety, but they need acidic soil and mine is pretty alkaline. Is it at all possible to amend the soil for this tree with sulfur and/or acid fertilizer? I also like oak trees, but I'm not sure if there are any that don't get enormous or can tolerant a bit of shade.

It would be futile to plant a tree not suited to the soil and impractical to change the pH. However, some trees with preferences are actually quite adaptable. You'll have to research. (I can't speak to the Tupelo.) There are lots of nice trees that grow in Chicagoland area. Maybe the Morton Aboretum or Chicago Botanic Garden has info for you. Or maybe you need to visit.