I would caution taking some of the earlier advice to get an analog scope to heart - they are honest opinions and all, but a car analogy is in order.
Qn: Hi! I want to buy a car, but not too sure if I need one with Electronic ignition and Traction control or not. Actually I don't understand traction control. Does it apply brakes to each wheel, or does it control the throttle?
Answer: I suggest you buy a older second hand model, before they had all these computers aids. You need to learn how to drive a real car before you get one into one of these modern ones. You will understand so much more about how they work, and how drive them properly. You can even pick up a really nice second hand one, even some real classics, dirt cheap!.
Or maybe you like biking:
Qn: I'm thinking of buying a full suspension mountain bike. I really don't understand about four-pivot rear suspensions - what should I look for?
Answer: If you don't know what you want in a full suspension bike, then you are not ready to own one yet. You will appreciate it so much more if you use a fully rigid bike on the trails first. Once you are able to ride that properly you will know what to look for in your next bike. You can't buy this sort of bike any more, but you can even pick up what was a really nice one dirt cheap on eBay!.
I say:
If you have the budget to buy new, see if you can pick up a low-end DSO that stretches your budget a little higher than you would like to go. The budget models from reputable brands are exactly the same as budget models of cars and full suspension mountain bikes - not the nicest to use, they have modest specifications, but perfectly usable within their limitations. Premium brands are nice, but usually have premium prices - you get more for your $ from a second-tier brand.
Old analog scopes on auction sites are dirt cheap on auction sites for one reason - because they are of little value. It hurts, but the market has speaks the truth - people who tell you otherwise have very different appreciation for the worth of these things from most, usually through nostalgia, passion, or a "I learned so much using one of these, you can too!" kind of way.
If budget is a problem, buy a second-hand DSO. If you can't find one you can afford second hand it is because they have real utility and value above what you are willing to pay.
Sorry if I am typing cranky - it has been a really hot & trying day here!