Allen has covered the key points, but I'll add my congratulations too.
I'll also add that "medium enlargement" probably means the prostate is more than 40 but probably less than 50 cc. A normal prostate is considered about 20cc to mid- to upper 30s cc.
In addition to reducing BPH, you will get the added benefit of a degree of prevention of prostate cancer from finasteride or Avodart.
While Avodart is theoretically better, at least on paper for impacting prostate cancer, finasteride is considerably less expensive as it is a generic. Finasteride reduces a protein known as 5-alpha reductase Type 2 but not Type 1. While Type 1 is more common in the skin but less common in the prostate, with Type 2 more common in the prostate, Type 1 is more associated with aggressive prostate cancer. Neither Type 1 or 2 are bad in themselves, but they convert testosterone to DHT, a much more potent fuel for prostate cancer.
However, since you are extremly likely not to have any prostate cancer, finasteride would probably work well. These drugs are both mild, but there are some potential side effects. Some of us grow more scalp hair, which is nice.
A small percentage experience less libido and perhaps some ED
(and some of us the reverse!
Either of those drugs should cut that PSA by about half or a little more, and you can track your new trend from that lower baseline. (In fact, if they do not cut the PSA by about half, that's a signal for more frequent PSAs to guard against prostate cancer.) For doctors who have kept up with research, those drugs make PSA trend analysis and DRE exams more accurate and useful indicators of prostate cancer.