Finding a doctor willing to do the operation isn't easy and it isn't cheap. Self castration is not safe or a good idea.
What mostly happens is that you can never have children of your own, you can also take a punch to the gonads

and you wouldn't have to shift them about or worry about them pinching or squeezing. These others aren't as certain, it differs, but all of them could effect you and likely would in the long term: Your hair will likely become more fine and soft, less coarse, even your whiskers(you'll be less likely to ever go bald, or if you're going bald you'll likely stop losing hair). Your skin and eyes could become more dry. You could become physically weaker and osteoporosis would be a concern. You'll likely lose energy, need more rest. You could gain weight more easily and have a harder time losing it, you could also grow breasts. You could become indifferent to things that currently concern you as a male, less motivated, less self conscious. Castrated men can still have erections and
can orgasm(sperm free ejaculate) but they have to work at it harder and it's not as fun. It's more common for the member to atrophy due to non-use. Without hormone therapy or with just a small dosage of hormones you'll experience what they say is a deeper calm.
You'd definitely experience changes. To quote a castrated blogger: "I don't really feel very male anymore. I also do not feel female. I do not know what I am, I just know it's not male or female. It's some kind of combination of the two - I like to think that I have the best parts of both genders without the worst parts of each." (He's not just talking about physical parts.)
If you want to experience it I'd definitely try the medication's first.