Anything that I want to be extra sure gets where it is supposed to I will ship UPS. Their tracking is easily available online and shows every stop made along the way so you know progress if it is going a long distance. Insurance for $100 is automatic and additional insurance is quite inexpensive. If you do have to make a claim the process is easily done online and they respond relatively quickly. You do need to be sure you have packed well if you are shipping anything breakable as the automatic response is insufficient packing, but that is easily appealed if you actually did pack well.
The office supply store I worked at for 19 years was a UPS shipping point for the public. In that time we only had about a dozen claims and people sent packages almost every day and lots of them in November and December each year. The one claim we had denied in recent years was one where the customer had indeed packed extremely poorly.

I noticed when I recieve some items I purchase. They tell me they will be coming fed ex. I have a tracking number. When I look it up, Fed Ex shipped to the largest the largest city from that point it's turned over to the post office

I ship both USPS and Fed ex. Depends on what it is and how fast I want it to get there. USPS is often more for big boxes. Unless you can get it all in a flat rate box, Fedex ground is cheaper. I have a Fedex home account, very easy to do, and I pack the stuff up, print out the label and take it to the drop off place. Works great for me.

I generally ship either PO or UPS. If it's a large item requiring insurance, then UPS. As others have said, they're easy to use. I've had some negative experiences with FedEx which is why I don't use them but I know plenty of people like them.

You can open an account with USPS and can buy and pay your postage and print a label online. The postage is also reduced if you do this online. Delivery confirmation is free. I have not requested a package to be picked up but it is an option. I keep a small supply of priority packaging at home then I just drop the pkg in the bin at the post office.