These are great questions! I don't always send out for printing, especially if it is less than 15 or so. I use a Canon MX series printer. I like it but it is a complete ink hog. I bought it because it was one of the first wireless ones and because it did double sided printing which few did back then. The printing is photo quality.
I had an Epson which I absolutely loved but if one cartridge ran out, it wouldn't let me keep printing until I replaced it which I found annoying.
For paper, I like Strathmore Writing Paper, 110#, in both white and soft white (cream). I bought it from the local print shop. It has a nice soft texture and prints well. Plus it is nice and thick but still goes through my home printer. I believe you can buy it online. It has a nicer texture than say scrapbook paper. And there is a wide range of envelopes to match.
I definitely gang up when I can and then cut with a paper cutter. I have a heavy duty cutter with an arm which cuts really well. If it has to be folded, I score it first on a Martha Stewart scoreboard and then fold with a bone folder.
I hope that helps!