A few years back, someone gave me a lee press. I was going to sell it and just for grins, I thought that I would try it out. The acid test for all presses is full length sizing large cases, especially cases that have been fired in an auto down to a min spec chamber. I picked up some 7 Mag brass off the range and tried to resize the brass on the Lee press. I got about 10 cases sized with great effort and then the handle broke on the Lee press...total loss.
If you are going to get into reloading, I would suggest that you buy a good top end press a RCBS Rockchucker, or a Redding, sorry to say that I have yet to try a Bonanza. I can't speak of the lyman, not familiar with them. I use a Rock Chucker and full length size the Magnum cases with ease. At my rifle range shack, I use a RCBS Jr just to seat bullets with when I am doing load development at the range, and a Huntington Press press to seat bullets when I travel to other ranges.
It is a real double barrel bitch to full length size cases with the RCBS Jr, and I mean if feels like you are going to pull the bench off the wall.
I highly suggest that you go on ebay and buy your press, you will have great savings.
Good luck and best wishes on your new adventure!