Most online PDF mergers send your files to a server. For a contract, a tax form or a bank statement that is a risk you do not need. A merger that runs in your browser does the same job and the files never leave your device.
The order of the files is the order of the pages. Check it before you merge, and open the result to scan the page numbers once. Mixed page sizes (A4 and US Letter) are kept as they are, so a page may look smaller next to its neighbour.
A PDF with an open password cannot be merged until the password is removed. A good tool tells you which file failed instead of producing a broken result.
Merging scans can give a large file. If you must email it, run it through a compress step afterwards and check that the text you need is still readable.
The Xargaar PDF Toolkit merges, splits, reorders, rotates and compresses PDFs, turns images into a PDF and adds page numbers. Files stay on your device. The free version produces up to 100 pages per output file.
Open the free PDF ToolkitNo page limit and offline use: the one-time $19 offline pack is here: https://xargaartools.gumroad.com/l/pdf-toolkit-offline-pack