DHO800 or SDS800X HD are actually off-topic in this thread.
The OP is talking about $250 for Scope with AWG + power supply OR AD3.
The devices mentioned cost double or triple that.
As I mentioned above, it's really about the question:
Benchtop scope with AWG + power supply OR AD3.
It is true that only the Hantek fits into this budget, but it is not really primarily about the manufacturer.
You may want something "better" than the Hantek at some point, but you may want a benchtop scope and a "real" power supply relatively soon after buying an AD3.
Nothing wrong with the AD3, that's just a guess on my part.
I have a rigol 1104z and an AD2. I'm still a student, but i do freelance repair and electronics design on the side. In my case, unless what i'm working on involves very low amplitude or frequencies above 20MHz, I use my AD2 most of the time, so even having a bench scope at hand, the AD2 sees more use in my bench. Of couse, everyone has different preferences when it comes to user interface or just the feel of turning the knobs/pushing the buttons in a standalone instrument, but when it comes to the capabilities of the instrument, the scope in particular, other than for those things i mentioned before (low amplitude, high frequency) what are really the downsides of the AD2? the only thing i can think of is the low waveform update rate, but even some instruments in the 2k$+ price range (tek series 2) exist with slow waveform update rate.
---End response to Aldo22
There's a lot of professional work that can be done within the bandwidth and vertical sensitivity of the AD3, and this is just about the scope "part" of the instrument. The add-on boards expand its functionality significantly, and you don't really need them, you can make your own impedance analyzer board, curve tracer board, and even your own specific purpose boards according t your needs.
You can also do Bode plots, and the differential inputs of the scope come in handy in all sorts of situations. for example, a while ago i took part in a contest by element14 about flyback transformers, and the AD2 made measuring the transformers very easy, and the differential inputs allowed me to measure both input and output current of the flyback converter, with the same instrument, which allowed me to show them time correlated which helped me better demonstrate the working principle than i would have been able to with ground-referenced single ended channels in a standalone 2 channel scope.
I think another significant thing to consider (if you care about stuff like this) is the user experience. If the options are an AD3 or a low cost scope, unless you have a strong preference for physical knobs and buttons, the experience of using the AD3's software "waveforme" is likely to feel a lot better than using a sub 200$ scope as it is intuitively laid out, very responsive, and it also has that "professional" feel to it, which to be fair can be a subjective feel, but most people have described low cost standalone scopes as having a very rough or unpolished "feel" to them. I think this part is an important consideration as having tools that don't feel good to use might result in the person not using that tool unless they have to, which could turn a fun hobby like electronics into more of a chore, OP may not care at all about this, so there's that.
What i would do, having that money right now, and needing/wanting a home lab right now, is try to get a used AD2 instead of the AD3,
a bench power supply(actually, i would build my own power supply. I did that as a project for a class years ago, and used that DIY supply for years until i got a "real" bench power supply) and a multimeter, then use that setup, and while that setup is being put to use, also start saving for a nice 4 channel standalone bench oscilloscope in the 400$ range like the siglent or rigol 12 bit offerings