I second everything parent said ^
You'll get a lot more utility and value out of software these days, but if you really want a hardware synth, the non-trendy 90s romplers can carry you far.
If you want something with knobs and analogue circuitry look out for some of Behringer's recent offerings on the used market. TD-3 is a reliable clone of the absolutely classic TB-303 and can be scored for under $100.
If you just want knobs and sliders, look at something like a used notation launch control xl.
If you want a full midi controller with keys, knobs, sliders, pads, maybe mpk mini? Nothing modern will have nice keys in that price range, though.
Plug in to your phone/iPad/laptop, download synth one or surge xl, spend some time mapping and away you go.
$100 is not a reasonable price point for good hardware that actually makes its own sounds, but who needs it when you have a super computer in your pocket.