Before I get into a 'healthy diet' I just want to say, do stronglifts 5x5, eat lots of calories (doesn't matter if they are clean at your stage imo, a calorie is a calorie is a calorie and you need lots of calories to help you recover, in increase your body weight, and especially to help your strength increase and build muscle mass). Perhpas avoid the worst sources (chocolate, hydrogenated fats) and look at nutrient rich foods like lots of eggs, liver etc. You should be drinking plenty of whole milk, milk seems to help more than its caloric value can account for and it is an easy and excellent way to add calories to your diet. 4.5k sounds good but you can shoot for more if you want. Who cares if you gain some fat now? Gaining strength and muscle at the cost of gaining some fat as will happen with the above suggestions, then losing some of the fat is much faster and more rewarding than gaining muscle and strength at a much slower pace and keeping calories meticulously low to prevent any fat gain. Seriously, a guy like you (skinny) will be able to shed 6 months of moderate fat accumulation in a month of eating a caloric deficit and keeping carbohydrates relatively low.
Right now:
Stronglifts 5x5, do it.
Eat lots, 4.5k calories sounds good. Make sure you get good amounts of protein. You want to consume quite a lot of carbohydrate due to its ability to further stimulate appetite and gain weight.
Don't be afraid of saturated fats, or cholesterol. Neither play a role in atherosclerotic plaque build up, arterial thrombosis, arterial swelling, endothelial damage, or anything else related to heart disease/blood vessel damage in which they are both implicated. Nor cancer, or infact, anything. They have vilified to sell you grass seeds (wheat, gluten grains etc) which make more money than livestock.
Drink plenty of milk (count the calories from the milk in your daily total)
http://www.stronglifts.com for the program and more stuff on gaining weight.