The Zombie Stack Exchanges That Just Won't Die
Because the budget and staff of either situation would be minimal, the major needs of such a system would be as follows:
Can pull MARC records from a reasonable variety of sources.
Please feel free to comment with additional qualifications if you think I've missed something.
LibraryThing provides this option and also has a product called LibraryThing for Libraries. Evergreen and other open source are, of course, free, it just depends how much expertise you have.
A library could use LibraryThing to catalog and maintain their collection. It would be for a very small library and a small collection, but it has been done and LibraryThing would help with that.
When you are looking for products that don't require downloading of anything, that gets into Software as a Service (or the "cloud" as it is popularly called). Many library ILS vendors offer this, Polaris, Innovative, even OCLC are good examples. They host everything for you. This might be out of your price range for a small library though.
There are also Open Source Products that you can download and set-up such as Equinox/Evergreen. The company can provide some support, but you have to pay developers to customize it to your need. There are hidden personnel costs in programming, but it is still cheaper than any of the larger ILS Vendors.
I guess it depends on how small a library it is; LibraryThing for Smallest, Open Source, then bigger vendors.
In my small corporate library, we use LibraryWorld. It operates in the cloud and is still allowable through firewalls. LibraryThing was an option, but as mixed media os not allowed through our corps firewalls.
Having been a developer on both Koha and Evergreen, Koha is still by far the easier system to install. On debian/ubuntu, among others:
sudo apt-get install koha-common
With significant adoption in India and southeast Asia, Koha is the go-to FOSS platform for small libraries. If you accept running a less than cutting edge OS for testing purposes, you can use existing install guides that literally show every command along way. That is, it requires only that you follow directions exactly. (However, this is not necessarily a reasonable way to approach production server deployment and maintenance.)
I don't have any direct experience with small ILS options. However, a couple of years ago I did a brief search for a very small school. Two of the options at that time that sound most relevant were:
I haven't used either of these but they sound like they might meet your basic requirements. Neither are free but, on the other hand, they appear to require very minimal in-house technical skills.
Evergreen and Koha are both very good open-source ILS options. However, I would hesitate to suggest them unless you have a couple people who are very comfortable with computers. The school I mentioned above use to have a full ILS system until the one person who knew it left. No one else had the time, inclination, or ability to learn it so they went back to using a physical card catalog.
NewGenLib is incredibly easy to install I found by following some basic instructions on their site, at least compared to Koha and other similar ones. Any question I had were responded to by the following morning (The developers are in India).
It has quite a nice back end interface, very professional but can take some getting used to. It can be integrated with VuFind too I believe.
Though as an earlier poster said, Koha might be easier in Ubuntu etc. The terminal installations are a breeze once you get used to them.
Our small religious library uses ResourceMate, which has already been mentioned by @gem. It's a useful database that (wonder of wonders) can still format and print cards for card catalogues. It can also be upgraded to read bar codes, track loans, patron fines, etc. I'd like to point out though, that the most useful tool, the ISBN retrieval, requires an ongoing annual support fee of about \$85/year. This also gets you excellent technical support over the phone. They have helped me through many problems and assisted in setting up reports and getting everything exactly as we want it. But if you are looking for 'preferably free', then an annual expense may not be what you want.