Check your option codes on the sticker under the hood, and match them up with something like https://www.stuttcars.com/technical/option-codes/986-00-02/ , should be able to tell if you had it originally. Look in the 510-540 range, the options are there I think.
Mine is a '97 that didn't have an alarm or keyless entry, and had a key like yours with just the light on it. I added them both very simply and cheaply following this thread: 3rd Party Keyless Entry DIY (Why Not?)
Yep that keyless remote system is hard to beat for less than $20 and a couple hours work. That's if you take your time.
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