Rhythmic thumping sound

I bought the vehicle used with high miles. It was a one owner car that has sat for for a few months, owner said he did regular maintenance and started it and drove it just enough to keep things working. I have had it in the shop on and off as things go wrong. So far. Plugs and coils, timing sensor, and just about a month ago I had to replace the tie rods and sway bar and alignment. The mechanic did let me know that the motor mount would need to be replaced eventually but I had some life left in it. I also know that the. Exhaust pipe bracket is broke. 2 of them I think. And here we are now with no idea of what's wrong. I will say before I get into the symptoms. From my research, some of the symptoms its having does line up with motor mount theory, such as the noise etc. But not the when and how. Just seems that symptoms of motor mount has a more narrowed down time and reason of occurring. Same as every other thing I thought it may be. Symptoms line up with a lot of things that could be wrong but not enough to fit, at least not for someone that can only use google. Google has helped me to narrow down time and occurrence and got me paying attention to the when why and how. I will give as much info as I can but please keep in mind that I have not wanted to drive the car often or on main roads for safety because I don't know what's wrong.

The symptoms and conditions that effect them as far as I can tell are:

Vibration/rattle from under car that changes in intensity (exhaust?) A deep clunking from under the car right front side nit sometimes seems like engine area but I don't think so. More under my feet than pedal area. The steering wheel it self not the column vibrates as well as the dash. Pretty much anything that normally has movement moves more. Other than that everything seems okay. Steering isn't effected nor does it want to pull one way or the other. I can take my hands of the wheel and it stay straight. The vibration starts once the car gets going gets going but barely noticeable. The noise doesn't happen at start up. Only once I get to about 25 mph. If I take my foot off the gas or brake to slow it stops. It also stops when I press harder on gas to speed up but starts again once it levels out. Turns and bumps does not seem to make a difference. I have not drove it over 30. Only back in my neighborhood streets. Sometimes I think something is going to just fall off. My fiance got under the car to look around and said he figured it out but he isn't car smart either. He said the pipes are loose obviously and the catalytic converter is hitting the heat shield (or whatever it's called) making the thumping sound. I only drive it maybe once a week to the gas station for 2 minutes there and back until I can afford to fix it. And there's a big difference in safety between driving with a loose exhaust and driving with a bad well. Anything else. So I wanted a second opinion. Thank you.