You'll get 250MB of storage for free. You can bump up to 6GB for $25 per year or use more than one Gmail account. Looks to me like 250MB will last a while. More on that later.
You can upload to Picasa Web two different ways. First, you can use the typical web upload for one file at a time. Ignore the #4 FAQ that says you can't. They just want you to download the Picasa desktop client. Which leads to the second method of uploading, using the Picasa desktop client.
If you already have the Picasa desktop client, you will still need to download the v2.5 beta. It has the feature you need to post to Picasa Web directly from the Picasa desktop client.
In a nutshell, all you have to do from the Picasa desktop client is to create an album and click on the "Web Album" button.
If you have the v2.5 beta Picasa desktop client and you visit a Picasa Web album that allows you to download, you'll have a link on that web page that allows you to download the entire album!
I have over 250 pictures on my Picasa Web and am using 25% of my 250MB.
You'll notice that the URL has my Gmail e-mail address so you may want to setup another Gmail address for photos (and darn, you'll get another 250MB for each one that you setup).