Depending on how many users your database may have to deal with simultaneously... if there is not a huge volume, you may be able to get away with hosing it on a FileMaker server. There are a number of people who have setup servers and charge a monthly hosting fee for you to host your solution. Develop your database as best as possible to be optimal for web performance and secure and simple enough that the general public can use it and then host it on a server.
What's your goal for a web presence? If it's just to have a gallery that people can do simple keyword searches on, then an off-the-shelf gallery website like smugmug.com may be an easier solution.
Filemaker server will get you to the web, either through WebDirect (filemaker layouts directly ported as websites), or via CWP (you'd need a web developer to make a website that connects and gets it's data from your filemaker database).
The filemaker feature set may end up being overkill for a simple gallery app. However if you want a highly searchable (maker, year, value, location, etc..) and more robust system, then filemaker could suffice for your needs.
I would propose another option, if this is not a "cart" and needing frequent updates:
Because web servers read/write 'files' as it's primary function, you may consider calculated HTML and export to pages. Then just upload as static web site.
Hello bright people....
I'm looking for "robust" that is for sure. Searchable by items via value, auto manufacture, mechanical style, and year. If I have to go light on the smart phones presentation, and then go heavy on the website information offering that is acceptable.
What would REALLY FLOAT MY BOAT would be a "thumb thru gallery" similar to viewing album cover art in the itunes library. I haven't looked into "photo gallery" software for a few years past, and will do that next week. I have a 10 day holiday break ( part time substitute school teacher ) next week and will look into those solutions.
I assume I'll need to do two offerings: 1) a smart phone quickie photo reference. 2) a detailed informative html website for laptops and desktop users/researchers. I'm a semi-retired art director with middle of the road skills with Dreamweaver, but very much in the dark when it comes to code.
BEVERLY: Will there be changes? No and Yes. Basic visuals won't change. A year from now I'd like to add an option to "tag" a item in the museum and let others know to be looking "high and low" for said item, and when found someone would like to purchase it. Evolving from a simple ID Guide, and moving forward towards a "wish list / for sale" marriage. A pretty museum is nice, but someone still has to pay the bills to keep the lights on.