Hi MD,
I am working on a very similar project now - knocked out a wall to open up my kitchen onto a formerly enclosed sunporch.
To install trim place a little bit of caulk on the backside of the trim and gently press into place. Then hammer the trim into your wall with small finishing nails. Don't hammer the finishing nail all the way initially - leave a little bit sticking out, or you'll damage the trim with your hammer. Then use a punch to hammer the nails down into the wood (about 1/8 or 1/16" deep into the wood). Finally, use a dab of caulk to cover up each little nail hole. You can do the same with your shoe molding. Then prime & paint. Your trim will look great.