I have an old HP110-110-3000 mini with a outdated Windows 7 starter edition to be replaced with a Linux OS equivalent. The HP-110-3000 has a half functional Internet connection, so I need to download this to mt Windows surface pro to a USB.
Suggestions anyone?

Looks minimal spec - 32-bit, 1-2 Gig RAM, 256M Intel GMA video chip; ugh. Small, slow hard disk.

I'm guessing most will recommend MX-Linux or AntiX - they're related and the latter is for older low-spec kit. Never used either.
Pick one and download the latest 386 iso (not x64), and stay away from gnome and KDE as graphical desktops, they will require way too much in the way of graphics support. On your surface use rufus or etcher to burn the iso onto a USB, and boot that on the HP. It will run in a live mode that runs in RAM so will be a bit slower than a real install but you can check everything works ok - especially video and wifi. Later you can choose to install when comfortable.

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Thanks
Would you have a link you can post?

Wouldn't have thought mxlinux.org would be too difficult to find.
Read the homepage, hit the download button. 32-bit XFCE looks like a good candidate. Might be more polished as a final product for you than antiX, but that's just a gut feeling.

With just 1GB or 2GB ram, add a swap partition of 2GB when you install it, especially if you intend using a web browser on it.