linear to bezier keyframe interpolation

I want to have a shape move from right to left but be linear in speed then when it gets to a point speed up and then slow down before going back to linear speed again.

I always struggle with understanding this. I thought I could have the first keyframe linear, the next one easy ease (hour glass), then another easy ease, and then finally linear, and that by selecting temporal (speed) interpolation to linear it would allow this. Problem is it changes the easy ease keyframes to linear.

Essentially in the graph editor I want a straight line and then an n shaped curve which i can modify the handles for to create the speed up and slow down speed I want, before going back to linear again. I have done this before but I’ve never learnt it properly and AE seems to do different things each time. How do I do this because it comes up a lot and is rarely explained in tutorials on youtube etc.

Also how do you move the handles so they have exactly the same percentage adjustment. Kust dragging them invariably results in slightly different values and if you are setting multiple keyframes - if you can have them the same percentages it would ensure everything is properly in time with one another. Can you type this in?