When flying by keyboard, it's important to note that the keyboard input isn't set up so that pushing a button slams on full aileron or elevator. The arrow buttons attempt to simulate smooth, fine-tuned stick movement by moving the virtual control stick slightly in the direction of the arrow-press. The problem with this is that you lose the easy ability to center your controls by letting them go, or more properly, by letting their self-centering forces guide your hand back to center as you reduce the force your hand is putting on the stick. On a keyboard, a couple button presses to the right will apply a slight amount of right aileron; to return to neutral, you actually have to press the left arrow button an equal number of times and for equal duration. Therefore, the left arrow button cannot be properly said to apply left aileron to the aircraft -- it reduces the amount of right aileron applied until returning to center, then applies left aileron.
Do you see how quickly that gets complicated? Believe me, when you get a few flight hours in and realize that maintaning a constant pitch does NOT mean maintaining a constant elevator angle; or that maintaining a certain bank angle requires NOT constant aileron pressure, NOT neutral ailerons, but something in between -- you'll be dying for that joystick, because you'll be lost in a constant game of arrow-presses trying to figure out whether your stick is centered, slightly right, slightly left, or who-knows-where.
Simulators do attempt to compensate for this lack of personal situational awareness by adding a meter of some sort to the cockpit gauges, so the keyboard pilot can see the virtual position of his or her control stick relative to neutral. But this is just one more set of gauges you need to watch, and as you'll see as you learn flying, a pilot already has plenty to watch and understand in the cockpit without having to scan one more set of gauges to figure out where his or her "virtual hand" supposedly is.
It is also possible to fly via mouse; but, because you will also need the mouse to look around and manipulate other controls and switches, that can get messy pretty quickly as well. Plus you still lack the ability to use stick pressure to center your controls.
All that being said -- I definitely understand how reluctant one can be about spending money on a new hobby, especially one which does sometimes have a reputation for being one that you can pour hundreds of dollars into if you want. But you can also get a lot of enjoyment out of it for ONLY the cost of the software and a cheap, $20 joystick. You're much less likely to get frustrated and quit if you make that rather modest investment. Many quality addons (scenery, aircraft, weather modules, and other tools) can be found for free, created by other avid sim-flyers for the love of the hobby. Then later you can decide whether or how much more money to spend on something more high-end -- or not.