It sounds like you have a 3 speed on the column and you are out of adjustment. If your bushings are worn and too sloppy then you with have issues shifting. Here is a source for bushings.
https://www.mcmaster.com/bushings/
I would start with the column in the neutral position, disconnect the rods at the transmission and place each selector on trans in neutral ( that is the center of its three positions), the rods should slip into the levers without any movement, there should be an adjustment to move the end of the rod to do so.
the positions of the levers are 1st, neutral reverse and on the other one it is 2, neutral and 3rd. I would replace the worn bushings before I started to check for the linkage being too sloppy. From what you are saying your issue going into second is the rod controlling 1, Reverse is not moving into the neutral position in time to allow the gears to go into 2nd, it's all based on timing. One set has to get to the neutral position before the other set can move all the way into the gear.