One of the simplest solutions would be to install the Gallery on the Synology server. It is a web based gallery software. It is listed on Synology list of Gallery software and it a rather proven solution. Since it is listed on the Synology list, it is actually tested by the Synology team. There are more Gallery software listed there, but I have no personal experiences with them. However you could take a look at them as well. We use Gallery at my work to share photos and it works without any problems.

The Synology server has a built in Photo software. I have tried it and I did not like it at all. It indexes all the photos on the Synology server and makes photo albums from it. I want to be able to select the best pictures to be on the public gallery. I also found the indexing to be very slow.

If you want to share the photos only locally, you could use DLNA. I use it for browsing the pictures from my Sony Playstation 3, which is connected to a projector. Any DLNA client could be used, such as Boxee, a Mac or PC. But judging from your question, you are looking for a web based solution. But the DLNA solution is something worth mentioning.

It is also possible to create web pages and enable the web server on the Synology. This is just a matter of a button click to enable it. This way you could create some kind of welcome page and entry point to all the pictures found in the Gallery. Please note that if you use a Gallery only solution, you do not need to do any HTML hacking and creating web pages. But if you are confident in making a web, this could be a nice addition to the Gallery software.

Using a web based solution, including the Gallery software, gives the opportunity to share the photos to the outside world as well. The Gallery software has built-in user handling, which force users to use a username and password. If you are going to share the photos to the outside world, I would recommend to register your server at DynDNS or similar. This is also done easy with the Synology management software. By doing this you could have an easy to remember web address.

As you could see there are a number of things and possibilities with the Synology server. I see no need to have a separate server to act as your gallery server, since you already have a Synology server that has a lot of power. I used to have a Linux server at home, but since I have bought my Synology server I do not have a need to have a Linux server. The Synology server is much easier to maintain, thus saving you a lot of time.