Wash the car well, clay it, youll need a lubricant to help the clay glide over the paintwork, use an old clean sprayer unless you want to buy one (see the Cleanyourcar website), i use very diluted car shampoo in a spray bottle but you can use proper clay lubricants or some people even use clean water.
Cut the clay into 3 pieces, warm one piece up using warm water, i run mine under a hot tap for a bit so it becomes soft, and mould it into a wafer thing. Then spray some of the diluted shampoo onto the paintwork and onto your clay bar face, all you need to do is rub with a very small amount of pressure back and forth. When the face gets dirty, fold the clay in half and then flatten it out again so it becomes like wafer again. it doesnt have to be mega thin, i keep mine around 10mm thick, not that that matters lol.
Bonded contaminates will be removed from the paintwork. My car is 5 months old, and when i got the car it was covered in what looked like rust and the odd bit of tar. Clay should remove all of this as it did with mine.
It takes time but its worth it.
After claying your car, wash it again. Dry it off. Move the car into a garage if possible.
Go round the car and apply a thin layer of SRP. Apply a small amount onto one of those applicators and rub in a circular motion or go back and forth or whatever you want, as long as the paintwork is covered, do the entire car and then remove using a towel. Dont apply too thickly as it is very dusty. Do not apply in direct sunlight. This is a filler polish, as in the swirl marks you might be able to see will be filled and not corrected, while SRP does contain some micro abrasives, it isnt really good for removing more severe wash damage or paint defects, it will however remove light wash marring, its a fantastic product. Avoid contact with plastics.
Once youve done this get the EGP and apply it to the other applicator, apply in back and forth motions or in straight lines, in an even fassion, and leave it to stand for at least 60 mins. From my experience, the longer you leave it the easier it will be to remove. If i remember correctly, i think the reccomended time on the instructions is 30 mins to 60 mins. I would leave it 60. Get a fresh towel and buff off, it should be fairly easy to remove.
If you want, you can apply a wax over the top of this but by no means is this completely necessary.
What ive told you to go for is from my own personal experience, its a great polish/sealant to use and i highly reccomend it to anyone wanting to spend a bit of time and a little money on their car, i have since moved onto different things and do not touch either of these products anymore, which is a shame in some respects as they are both very good. These products are by no means the best out there either, and different people will give you different advice, but i think from what your after and the budget you have, this would be a great place to start.
What products do you have for washing?