Removing swirls on a " budget " aka with normal priced AutoZone bought products is easy .

First step after washing / claying and removing tar and bug splats with tar/bug remover is to clean the paint job

First let me show you guys this item at overstock.com , very good price for the " occasional detailer " Its a waxmaster 7" random orbital w/$1 shipping . Very good starter kit ( unless you can afford much better )
http://www.overstock.com/cgi-bin/d2....cid=60488&fp=F
You want to do heavy swirls with this item and the terry bonnet that comes with it . realize that you MAY be adding more swirls to it , but since the ones you have are probably very old , removing those 1st is what NEEDS to be addressed !
Do small area like 2ftx2ft at a time , move onto next area . Apply your swirl remover to the pad in a x , not to the car and rub it around in your area .
Dont do it in direct sun .
Meguiars 3-step is okay , but unless you want to stop with this and not use a protectant to not have to wash/wax every month - skip step 3

Step-1 Paint cleaner
Follow directions
Optionally this product works better / faster , BUT really needs to be applied my machine 3m for light cars orr 3m for dark cars
Aftet step 1 - go over the car again with the same swirl remover , BUT by hand on areas that dont look the same as the machined areas . You want to use a hand terry applicator available in the wax section of any AutoZone / etc such as turtle wax round ones or these round ones
Step-2 seal & glaze
For this stage , you want to sue the polishing bonnet from the kit 1st stage .
Also optionally if your paint is awesome , use these bonnets after using your regular ole polishing bonnet in kit . Still works doing only once , but better more through results going thru different grades of pads
Follow directions on the label
After confident it is even and swirls are gone ( except maybe when viewed at extreme angles ) go over again by hand and same product .
Nice hand applicator here for this polish stage ..
NOW - wash the car again the next day using ONLY a car wash shampoo such as these Dont buy trurtle wax , NEVER use dish soap again and etc . etc ..
Have soapy lukewarm water in one bucket , clean cool water in the other to rinse your wash mitt with every round change .
Use a chenille wash mitt
and special drying towel / suede chamois

Let car air dry a few hours , then get ready for final stage of sealing / polishing

Make sure your foam pad the bonnet goes over has been washed with Dawn and dried the night before . face up
Use the sealant of your choice , but it must be a good one .
That's why I love the eagleWax product . If your car paint is great now , no chips , nicks etc and you want to KEEP it that way - go for teh Kamikaze and their suede microfiber towel ( must use )
If not , and you still want your car to be sealed and protected , use one of their lesser / cheaper polymer sealants with less duarbility .
You need to 1st apply it with this bonnet 1st , then wipe off with the suede microfiber after giving set time on label . Then apply by hand gently onto every edge with their suede microfiber and wipe off with the same towel ( folded under clean section )
After this stage you can apply a wax also , just wait a couple days . Use a good polymer wax like NXT or EagleOne nano or DuPont w/teflon .
Then you can use finishing spray and your microfiber sueded towel to touch up every once in awhile for extra gloss , depth and shine .

Note - main reason to always do again by hand each stage is as was said earlier always go by working the hand pads in up down motion , finalizing with a one direction wipe or two . This helps keep swirls out , and make it easier at the next stage if more cutting / filling it is needed to go across the path of the last step and is really the only way thats effective .
Also when going by hand you can work the edges of your paintwork without fear of staining rubber / plastic so easily with the buffer .
note # 2 - before waxing or when buffing any stage and after wash / clay apply a water based rubber / plastic protectant to your trim pieces 1st before doing paintwork . Armor-All original is water based . A lot less work just soaking them down with a quick excess wipe then scrubbing wax and cleaner stains out .

Dont do any of this in direct sun light either btw . Unless label specifically says its okay or beneficial . Usually only a true cleaner free sealant such as the EagleWax highest two lines will allow this or recommend this .
Anything you guys need to know ask ..
There are more expensive products out there , but these products and in these steps with the right pads will do a damn good job .
All for under $100 up until the EagleWax part - but thats good for 3-4 apps that last at least 1-2 years each .