You definitely sound like you are eating enough that you "ought" to be gaining weight.
Personally my advice, would be let it be as long as you aren't currently running into health issues. Within a few years when your metabolism slows down you'll have to start eating healthy like the rest of us
If you really, really need to put on the weight its actually going to be a bit of work. A lot of people have points where there body just doesn't want to hold extra (healthy) weight. But if you make an effort to add in a shake or a glass of milk to every meal (at least 3-4 times a day) You should see some progress.
If you really really aren't seeing any progress, a trick some bodybuilders who are "hard gainers" use is setting their alarm clock, or drinking a lot of water at night, and getting up once or twice a night to eat or have a shake.
As far as red meat vs white meat, white meat tends to be leaner (meaning less fat) but red meat tends to take longer to digest. As long as you're keeping a varied diet, you should be fine.