As for which Ruger *model* to go with, I don't think you can go wrong with the 77. They're tough to beat, IMO. You might need to get some trigger work done, but that's not a given as some might have you believe. The 77 target/varmint triggers are excellent. Of the last two 77 Mk II's I ordered new (25-06 and 7 wsm), one had an outstanding trigger and the other was fair to good.The25-06felt like it had either work done already or a custom trigger in it and the7wsmhad a decent trigger for hunting. The 7wsm's could be better, but it wasn't bad, by any means.
I don't know anything about Ruger's lever actions (96) except that I think they're ugly.

The new Mini-14 Target is quite a rifle though, from what I understand, although I'm not a fan of using a .223 for deer. Looks like it would be an excellent choice for prairie dogs/coyotes/etc or just the fun of shooting.
The Ruger model I'm in love with, though, is the #1. Unless a single shot is absolutely not your cup of tea, that would be the way to go, IMO.