B.R.
Congratulations on getting a house!
You either have time or money.
I never had the money, so I spent the time cutting up my own tree limbs and branches with a cheaper electric chainsaw for the big stuff and two different sized pruners for the smaller stuff. You will need these tools anyway. I got the low end electric chain saw from Lowe's or Home Depot and my pruners from Big Lots. One pair is small hand held. the other is longer extendable handles with a bigger pruner. Just don't twist the pruners and they'll last several years.
Don't be in a hurry and it will get done.
If you have plastic trash cans or can invest in two, put it in those and yard waste will pick them up every week. Or buy bags. Or you can bundle and tie with natural string, no plastic. This is the cheapest way to get rid of it fast.
You can run the two lengths of string all the way down your driveway and make several bundles at a time, leaving a space between each bundle. Then cut the string between bundles and tie each one. Step on the bundle before tieing, so bundle doesn't become too loose and fall apart.
Yes, be careful of those wood siders! If you open up the area a bit by moving some big pieces and getting sun and air in there a day or so first, a lot of those creepy crawlies will leave.
Tree trimmers and landscapers are VERY EXPENSIVE! Buy the tools at a micro fraction of the cost and just don't be in a hurry. There's always next year!
Also, I had several stumps in my yard and a tree grinder is expensive, either renting the tool or hiring someone. If you dig a trench around the stump and let it be a few weeks, it really loosens up, but it will still be hard but possible. Don't try to remove it all at one time. I also put stump rotter on a couple of stumps with an upside down pot over it so the dogs didn't get into it and let it be for several months. It breaks it down considerably. I am 53 with arthritis, my adult daughter is pregnant, but we were able to remove half a dozen tree stumps and massive bush root balls by doing this little by little.