I have an Romanian M44 with a lot of character, and I just bought a beautiful arsenal-refinished M38. The iron sights are good enough for easy 100 yard shots. I have Darrell's scout scope mount, and a Simmons 4x pistol sight, but I haven't had a chance to put it all together with the M38.
I strongly recommend getting some training in safety and marksmanship. I was extremely lucky in having a rifle club in my middle school (Fairbanks, AK). Unfortunately, such opportunities are less frequent now. Look around for an NRA sponsored class or an experienced friend or family member to help you.
That being said, I think an M-N is a great choice for you. It is a sturdy, yet elegant design with a lot of history behind it. It is great for the budget-minded and you will probably never outgrow having fun with it.
About the only negative thing that is normally said about them is that the bolt is hard to operate. There is nothing really wrong with it, Mr. Mosin just designed it that way. I think mine are still breaking in after 50+ years!
The average surplus M-N will not be a tack driver, but I think that's fine for target shooting and blasting. I think accuracy requirements are a bit snob-driven on some of these boards anyway. You could certainly go hunting with it in the future if you don't exceed the limitations of the gun and your experience.
Load carefully to avoid rimlock, and take advantage of the surplus ammo market. I like the 196 grain Yugo surplus for plinking. Treat all surplus ammo as corrosive and look up some cleaning tips on the milsurp boards. I clean with Windex and/or boiling water followed by Breakfree, and have never had a problem with rust. Always clean right after shooting, and you will be fine. Shoot only in safe places, and have fun!