One thing that is definately worth investing in, is a pullup bar. Some are available that kind of hook onto the top of a doorframe, without having to me attatched or twisted outwards until its pressing against the doorframe. Careful of potential damage to the door frame.
This allows you to perform chinups and pullups which are excellent at increasing strength and size in the upper back (specifically latissimus dorsi), as well as in the biceps. Pushups and crunches do your 'push' (triceps and chest) and your rectus abdominus. Really you should add in the 'pull' (this can be from pullups) and something for legs, like lunges or squats.
Also you say situps, if you're referring to proper situps, these put dangerous loads on your spine and use your hipflexors more than your abdominals which is what I am guessing is what you want to build, the suggested 'safer' alternative are crunches. However there's evidence to suggest this repeated spinal flexion is damaging. I would highly reccomend buying an ab wheel, these are fantastic. Other forms of core training are planks, side planks, bird dogs, and a modified crunch 'mcgill curlup'.
In a couple of months? It depends on a lot of things really, including your genetics. I personally can't imagine you'd see much of a change in 2 months for your muscle mass, but you can see yourself improving at the number of repetitions you can do/weight you use, etc.
8-12 reps, for 3 sets is one of the optimum ranges for increasing muscle mass, so if you can do 3 sets of 12 pressups, slowly with good form then they are too easy for you. You can increase the weight with a rucksack that fits over the upperback/shoulderblades (not lower back) and doesnt slide about. You can add weight into this to make pressups harder. One way you can do this is water containers. 1litre of water = 1kg.
Wide pressups work the chest more, and narrow ones work the triceps more. Dips are also a good 'push' exercise which i would reccomend.
You could do something like
Monday: 3x pullups, 3 x chinups, 3x assisted pullups (with a chair to help).
Wednesday: 3x pressups, 3x wide pressups, 3x dips.
Friday, 3x Ab rollouts, side planks, bird dogs, lateral raises and lunges.
(the ab rollouts will work other parts of your body too, like triceps. So this may affect your push day).
I have done something alont these lines but have switches about with them. Maybe this is a terrible routine. You could do a fullbody workout 2 or 3 times a week. I'd reccomend checking out scooby1961 on youtube, his website and forum.
As for protein, there's a lot of information about. Have a look around and make up your own mind.
Although the effeminate nature of my username may suggest otherwise, my gender actually falls into the male category.