Please recommend me a web host company to host my pictures.

www.pair.com (I've been a happy customer of theirs for 6 years, theses guys really know what they are doing)

EDIT 01-25-2010:www.pairlite.com. Same stability as Pair, but at a lower price. Most notable differences between "lite" and their regular service that I can tell is support is via email only, which has always been great for me, and they utilize fixed limits on these "Lite" accounts.

www.ithought.org (a one man show, but he really knows what he's doing) Almost went with Chris, but decided to go with a VPS, see next comment

www.linode.com (if you're into setting EVERY THING up your self, installing all software (except for the initial operating system), maintaining all software, updating all software (web server, database, etc) and working at the command line. This is where I'm moving all of my stuff to.
EDIT 05-06-2010, added link to performance comparison of various VPS providers:
http://blog.linode.com/2009/12/04/linode-stomps-competition-in-performance-benchmark/

www.slicehost.com (same as Linode, but Linode is a better bang for the buck)
EDIT 05-06-2010:
You'll probably be more inclined to use Linode after looking at the performance comparison above. I can only say that my experience with Linode has been great and I continue to see person after person praising them in their forums.

The next suggestions I've not ever used these and never will, I just know there are people who do have success with them.

If you want quality, reliable hosting, these first 4 I mention here are the only 4 worth considering in my opinion. Granted the last 2 are more of a DIY route and really only for more technically minded and aware people.

www.dreamhost.com (some people are successful with using them, really seems to be the luck of the draw on which server you get planted on, good luck)

EDIT 10-08-2009: Due to Dreamhost's incompetence with migrating a few customer's sites I've struck them from my list. I had a feeling this was going to happen at some point based on just watching issues they have posted on their status blog. It gets down to you get what you pay for. Every host does have it's share of issues, but it's how that host deals with those issues that counts. Whether you view this as far or not about Dreamhost, it's my opinion and my opinion is what matters to me

EDIT 08-14-2009: I've struck out bluehost and hostgator. While people have had success with them, their customer service appears to be sub-par.

www.bluehost.com (some people are successful with using them, really seems to be the luck of the draw on which server you get planted on, good luck)

www.hostgator.com (some people are successful with using them, really seems to be the luck of the draw on which server you get planted on, good luck)

BE AWARE: The hosts that offer unlimited STORAGE are offering just that STORAGE (disk space) NOT unlimited files. As Host Gator's customers have come to realize since Host Gator has been cracking down on people with lots of files. Lots of small files versus fewer very large files drastically reduce file system performance.

My opinion: DO NOT use Yahoo or Godaddy EVER for ANYTHING

You get what you pay for. There is no truly unlimited host, if your site takes up too many resources and you'll be dropped. I know people who have had their accounts canceled at Dreamhost, Bluehost and Hostgator. Though I know others who have several 100 thousand images hosted at Dreamhost (saw someone making such a claim in these forums just the other day), so YMMAWV (your mileage may and will vary) at any cheap host

____________________________________________
Like Gallery? Like the support? Donate now!!! See G2 live here

There are hosts who have "one-click" installers. In my experience, I've found they are either out of date (by a long time), or enable features they haven't tested on their servers and they don't work "out of the box"

Do yourself a favor and only ever download Gallery from here: http://codex.gallery2.org/Downloads and install it manually, it's really easy actually.

At any host, you'll need to create a database, this can usually be done through a control panel that the host provides for you to log into and manage aspects of your site and account.

http://codex.gallery2.org/Category:Gallery_2:Installation

If you have ssh access, it's really easy (after creating a database for Gallery to use) if you're comfortable with the command line

____________________________________________
Like Gallery? Like the support? Donate now!!! See G2 live here