You need to use a backend technology to perform server side searches.
SQL is really good for searches. It means "Structured Query Language" where the query is your search parameters.[
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With or without a database, you will need some back end language. Performing the search in jQuery is a really bad idea. All of the products will have to be loaded at client side for every search.
PHP is good for small sites where security isn't an issue[
^] and it can be run on any platform (win, unix, etc). I prefer ASP.NET written in c# but it can also be written in VB. This can only be run on a windows server (atm).
To use .NET (ASP, VB, C#), you will need Visual Studio. You can get Visual Studio Community for free.[
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You will need to brush up on these technologies. There is a steep learning curve but getting a basic website up and running is actually pretty easy. You will be able to turn your html website into a Visual Studio project without converting anything. You can choose to convert your entire website to a web application (making backend dev easier) at any time or not at all.
More on opening and converting website in Visual Studio here[
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Post a new question or let me know if you need help setting up. Once you have the setup, post a new question to ask how you can write searches in your chosen language