You can do a chemical decontamination fairly cheaply and the benefits of this would be that the sealant or wax will bond better with your paintwork, the only thing i would do is use a clay bar unless you fancy giving the car a one step machine polish as the clay bar will inflict some marring (scratching).
I could recommend a number of different methods but i'll try to keep the cost down here:
1) Pre-wash, if you don't have a snow foam lance then you can use a citrus pre-wash applied through a garden pump sprayer or some Bilt hamber auto foam diluted to 4% again applied through a pump sprayer.
2) Contact wash with two bucket method where you have two buckets with grit guards in the bottom and what you'll do is fill both with water, add shampoo to one of them and use the one without shampoo to rinse/clean your wash mitt after it has touched the car. Most have a dedicated third bucket for cleaning the wheels as as well as separate brushes and mitts so anything stuck to the wheels will not scratch you paint work.
3) Dry the car with a drying towel.
4) Then apply a fallout remover like Bilt hamber "Korrosol" this removes any iron particles bonded with the clear coat like brake dust. Let that dwell but don't let it dry then pressure wash the car over and dry it, if you feel like it needs doing more than once then repeat. If you have a white car you'll near instantly see red bits appear on the paintwork to show you it's working if you have a black car then you'll miss the magic unfortunately.
5) Next is to treat the paint work with tar remover and most of us would probably recommend "autosmart Tardis" and all you need do is spray over a few panels at a time leave to dwell and rinse off. This will help remove any bonded tar with paint work again if you have a white car it's easier to see the little black spots that gather mostly around the lower portion of the car.
5.5) When you have completed the above steps i like to give the car another little clean personally but if you feel you have rinsed everything off well enough then you may not feel the need to.
6) Now you have nicely decontaminated the paintwork it's really up to you whether you'll feel the need to polish the car, if you do then it's worth considering claying with a soft or regular clay, if you don't then go to applying LSP, personally most car will benefit from even a light pass with a DA (machine polisher) and a one step polish like Scholl S20. A one step polish has a bit of cut to remove light marring and will polish the car too hence one step a bit like wash and go shampoo.
Most hand polishes like autoglym super resin polish are perfectly fine to use too but what they contain are "fillers" to mask the fine scratches which are great! but don't last forever so you may find yourself polishing every few months, personally fillers and glazes can affect the longevity of the LSP not allowing to bond as well.
7) This is a step some do and some don't but before applying your sealant or wax (LSP - Last Step Protection) it can be a good idea to use a paint cleanser or IPA diluted 70% with some DI water and the reason for this is to remove any a greases that may be left on the paint work which will allow your LSP to bond better. HOWEVER if you have use a hand polish or glaze then i would skip this step as you'll just remove the polish you have put on, really cleansing the paint is for after machine polishing.
8) last up is to apply your sealant of choice and you can't really go wrong with BH double speed wax as it is a great all rounder.
I think i typed a bit more there than i intended too and without seeing the car we're just advising blindly but i hope it helps and there are some bits you can pick out of it.
