First put the squirrel gun away it has it's place but dog killing isn't it. To answer your question yes it will kill them. I've seen the guys who butcher cattle shoot them in the head. However, you wouldn't use a 12lb sledge to hang a picture would you? Different tool different job.
Early morning and late evenings right around dark will be you best chances. Take which ever rifle you're most comfortable with, if you expect close shots take the 30-30, if long shot can happen take the 270. I'm assuming they're deer rifles and your deer bullets will work just fine. If you were planning on selling hides or anything like that then, you would worry more about bullet selection. If there's a sportsmans warehouse or something similar close to you grab a couple calls and a dvd or two. Randy Anderson is my favorite, they've got a combo pack with a call or two and a dvd for around $40 I picked on up a couple months ago. Don't worry too much about learning to make howls and all that just yet. Start out with a couple closed reed distress calls, rabbit and fawn sounds will suffice. Grab a bottle of scent killer probably 20 diff companies making it now, I've been using dead down wind got a good price on a combo pack, used scent away for yrs.
The most important thing to remember is have fun, keep your head up and keep trying. I hunted with my dad and a few friends for 3yrs before we ever called one in. Sneakiness is the key don't quickly walk through dry leaves, slam truck doors ect... When i make a stand I sit for around 30min, I'll sit for a couple min to just watch the area and let things calm down, slowly scanning with my binos. Make a series of calls softly for a minute or so, wait 5 and make another series louder, so on and so forth till about 20 min has past. The last ten or 15 I sit quietly just watching, remember to keep you eyes peeled sit as still as possible, only eyes doing most of the scanning. Some predators will come in almost immediately and just about run you over some take longer or have to cover more ground to investigate your calling. I usually hunt with a rifle and a shotgun, shotty up and ready, rifle on my bipod ready to pick up and make the shot if one hangs up. Remember movement is what will get you busted every time. Hope this helps, there is tons of info out there so read and study up as much as you can. You can get as complex as you want into wind reading and decoys and blah blah blah but, keep it simple and have fun!!! Bring a buddy or neighbor or some one with you to share in the experience and two sets of eyes are better than one.
Good luck, happy hunting and welcome to the most addictive pursuit in the woods.
