If you weren't ready to stop by the end of your longest rides, it sounds like you're in good shape for now. Lots of randonneurs love their older frames; there's no reason to get something else until there's something specific you want out of it. The only things you really have to have for long distances are a working bicycle, a way to carry whatever food and water you'll need between stops and/or services, lights if you ride at night, and whatever other safety gear (helmets, reflective stuff) is required by the event in question. Everything else is up to you.
Most of us find cycling clothing to be more comfortable than "civies" for long rides, even if we commute in normal clothes, but we aren't you. Wear what you've got until it starts causing you problems, then replace it.
Lots of things might make you faster or more comfortable, such as clipless pedals with cycling shoes. Lots of things can be upgraded or lightened, like tires, gearing, wheels etc.
The argument for buying/upgrading what you need to as you find things that could be improved is that you'll have a better idea of what you need. It's certainly more economical than going out and buying what people say you are supposed to have, only to find that it doesn't fit or doesn't quite work and you have to change it anyway. Solve problems one at a time as they crop up, which they very well might as you start increasing your distance. Your needs and preferences will change as your habits and experience do, and there's no off-the-shelf substitute for that.