The plane is probably going up and to the side because of a combination of two factors, at least that's what i'm suspecting.
One is caused by the propeller and it depends on which direction it's turning (some planes will swing left and some will swing right, depending on the direction the prop turns). In some planes this is more pronounced than in others and it's also affected by your throttle settings. For example, a late war BF109 will sway much more when you use high power (stronger engines, more torque and so on).
The other (the upwards effect) i think is mostly about trimming. Think of trim as a way to tell the aircraft at which speed you want it to fly hands off. Just like in a car, you need more power to go uphill. The difference is that the car sits on the road, but an aircraft can "make it's own uphill road" so to speak. So, if you are trimmed for a slower speed (say, 70% throttle) and then you increase power (eg, 100% throttle), you create an excess of power and the plane will climb. Similarly, if you are trimmed to fly at 400km/h, you reduce power and your speed starts dropping below that speed, the plane will dive on its own.
Of course, if you add too much down trim you are telling the airplane to fly at speeds that it can't maintain in level flight, so it will keep on diving until it crashes. Similarly, if you add too much up trim you are telling the plane to fly too slow. The plane will nose up and try to keep it there, but at some point it will either stall or gently drop its nose, because by going up for so long it goes below the speed specified by its trim settings and wants to dive again.
Don't worry about trimming for exact speeds as there is no documented way or any tables telling you how to do it. Just experiment with it and you'll get the feel of it.
Also, when you want to keep your speed high, trim the aircraft to cruise on the step. For some reason i don't completely understand, some planes can't attain their highest speeds if you just level off. It's better to climb a bit higher than your intended altitude (500-1000meters), level off to increase speed and then dive back to your target altitude to get even more speed. Then you trim as needed (usually it's nose down since you picked up speed and you want to keep it, ie you don't want the plane to start climbing again) and you keep cruising at your new increased speed.
This is called cruising on the step and it's a recommended procedure for many aircraft in real life as well.
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