So I set out to figure out how to upload and resize to the target size automatically. Previously the Picasaweb web upload offered to resize automatically but that capability is now gone. Odd but oh, well. But I figured out that the Google+ photo upload process does resize automatically. But (isn't there always a "but?") Google+ wants to share the photos automatically and doesn't give you good tools to manage the sharing.
So here's my trick. You need a Google+ profile to make this work.
Login to your Google account. This is probably your Gmail account. Go to your Google+ "Photos" page (https://plus.google.com/photos). You may have to join Google+ the first time.
Click on "Upload new photos."
Drag photos or select them from your computer.
Here's how they'll look uploading. Click "Create album" when they're done.
I don't tag people in my Picasaweb albums so I "Cancel" here.
Now here's the fun part. This prompt about sharing is about sharing using Google+. Click on "Cancel" here. You'll get to specify sharing in more detail in a little bit.
Now browse to "https://picasaweb.google.com/home." Your new album should near the first of the list.
Select it and you'll get the Picasaweb sharing options at the right. Click on the "Only you (edit)" way up near the top right.
Whew! That's what you want. Down at the bottom is a drop down for "Visibility." That gives you more choices that just Google+. Notice just below this drop down is a check box to show or hide the geolocation data.
Make your choices and click on "Save changes" and you're done. If you've chosen the "Visibility" of "Limited, anyone with the link" the link is about halfway down the page on the right when you click on "Link to this album."
The link will look like "https://picasaweb.google.com/[your Google+ profile]/[album name]?authuser=0&authkey=[authkey]&feat=directlink." I know the following is confusing but when you share this, add "&noredirect=1" at the end. Google moves in mysterious ways. What this does is force the presentation to be in the Picasaweb format rather than the Google+ format. It'll work fine if you don't so don't sweat it.
These photos are resized to 2048 x 2048 or less and don't add to your Picasaweb quota of 1 GB. Unless your originals are smaller than this you shouldn't depend on this process for backup, just for free sharing.