Basically, the first number is the standard viscosity rating and the second number is the viscosity rating when it arrives at engine tempurature. I personally use 15w-40 for the fact that my vehicle is a higher milage engine, and a thicker oil is harder to blow by rings and older seals. I would stick to the main brands of oil like penzoil/quaker state which don't have additives in them. If you opt for oil like Slick 50 or other exotics oils they have solids in them like teflon which can clog up your filter and other additives that can coat the inside of your engine.
If you want to play it safe, just stick to what oil your manual asks you to use (probably 10w30). If your milage is starting to get high, move a step up in viscosity.
As for installing it yourself, yes it is pretty straight forward. You can basically just pull off the PCV valve itself. You'll have to use pliers to take off the hose clamps of course. Take off the hose and make sure that there's no obstructions in it. You can spray the intake cleaner inside it and blow it out with compressed air (if you have access to air, if not thats ok). Just make sure you put the hoses back the way they were and make sure they're back in place.
Next step as I explained before is to clean the throttle body and intake, as you dont want all that gunk plugging up your PCV valve again. So take off your intake tube and just spray intake cleaner inside the throttle body and on the back of the butterfly valve. Scrub what you can with a tooth brush and spray some more until it starts dripping out the throttle body. Then start up the engine. (your car will probably sputter and stall, that's normal) rev the engine a little bit until it blows some stuff out your exhaust and runs smooth again. While its running, open the throttle body a teeny bit and spray some more cleaner inside. And just do that until it looks pretty clean inside the intake. Oh and by the way, cleaning the throttle body is NOT something i would recommend EVERY time you change the PCV valve, as it can do damage to your catalytic converter if you do it too much. Just once is fine and wont hurt. and keep on top of replacing that PCV.
If you need anymore help, let me know.
In that diagram, #3 is what you wanna replace, and make sure pipe #4 and #6 are nice and clean.