That was my very first shotgun.. 28" modified.. Loved it and still do..I learned to shoot with that gun.. Never had any jamming issues etc.. When I got into crow hunting it was limited with 3 shells maximum.. So I ended up trying other shotguns that held more rounds..
I have one that my father bought in early '70's. I have hardly ever used it. They were inexpensive guns that work well but were not particularly reliable with a lot of use. If you can find it cheap enough buy and shoot it. Parts may be hard to find. Here is a good read of one person's experience which is very thorough.
If your Ithaca 51 ever breaks, DO NOT send it to Les Hovencamp, Ithaca, N.Y. He charged me $142 just to install a magazine spring in a shotgun of mine. The spring cost only $10.00, I know, as I bought a new one the day before yesterday (Tuesday) for the same gun. His cost included shipping, but that still seems like a hell of a lot for a 3-5 minute job.
If anyone mails a gun for repair to a gunsmith, the experience may be like Steve Mcqueen quoted in the movie "Magnificent Seven". Steves quote..."a fellow jumped out of a high rise building. On his way down, people on each floor kept hearing him say, "so far, so good".
Steve also had another quote in the same movie...goes like this..." a cowboy took off all his clothes and jumped into a mess of cactus. Somebody asked him why. The cowboy replied, " it seemed like a good idea at the time".