I remember my first attempt at a slipjoint. I had some very good plans from a well known maker (Don Robinson), and had made (and sold) several fixed blade knives already. I had also done a fair amount of research on slipjoint folders. I wish I could say it came out at least usable, but I made so many mistakes on first go round, that I never did even finish it. I later attempted a handful of other designs that more closely resembled a working model, but even they were not even remotely close to what I would consider a mediocre, working slip joint, much less one that I could sell. At the time, I had a decent array of tools, and much experience using them.
At the end of the day, it just boiled down to not knowing what I didn't know, and having to work out certain problems that reading text on a forum couldn't really solve, without the hands on experience.
Presently, I've now made several slip joints and sold an even smaller amount, but it took quite a while and a LOT of experience to get here.
All that said, do I think somebody CAN start by making slipjoints? I suppose. There are a very few select makers who started with folders of one kind or another and made it work. Granted, most of them had very specialized backgrounds (i.e., machining experience), as far as I know.
Now, do I think somebody SHOULD start with slipjoints? Not so much, or at least not without some reasonable expectations.
As for tools, I suppose it wouldn't be impossible to make a working slipjoint with minimal tools. I agree that a decent drill press should be on the top of the list. For a folder to work well, all holes need to be perpedicular and round. Reamers should be used to ensure holes are accurate. Any stock/material should be perfectly flat and parallel as well. If I didn't have a surface grinder, I'd start with some precision ground stock. A surface plate or a flat piece of glass with some sandpaper laid on top can function as a poor man's surface grinder. This can also be used to CHECK for flatness. Calipers are a good way to check material specs, make sure pieces are parallel, and the same thickness.
Stock removal and shaping can all be done with hand tools as well, though I personally would rather use a grinder. Get some quality files and sandpaper. A lot of beginning makers use a drill press to drill around the periphery of the pattern they want to cut out, and then use a hack saw to "connect the dots".
Taking apart some existing, working slip joints will help understand a little about how how the parts fit together and need to be made.
I'd wager that your first attempt may not come out anything like you'd hoped or planned, but stick with it. After about a dozen tries or so, you should be seeing some noticeable improvement.

The main fear is that, by starting with such high aspirations, you'll burn yourself out with disappointment before you've even really started. Personally, I would set the bar for my first knife as low as possible. Make something dead simple with the tools you have, and learn what you need to make the next one better. Let yourself taste a little bit of success first, no matter how small, and then start working your way into a slipjoint folder.
When it comes time to start your first folder, eliminate as many variables as you can: Start with a known pattern or plans, use precision stock, keep it simple. We all start somewhere, and if you keep at it, you'll get there eventually.