Mzumel,
I just did my oil on Sunday .... Here is my suggestions:
I bought a Mazda oil filter .. 7 bucks at the dealer.
I used Castrol Syntec (not a full synthetic - AND I dont care what anybody thinks of Castrol, or not using full synthetic .. I change the oil every 5000, and have never had any problems) You can use whatever oil you want. The dealer just recommends 5W-30, at least a synthetic blend.
Get the Mazda Oil Filter Wrench!!!!!!!! I can NOT stress this enough. I think its a 74-76mm 14 flute wrench. The 15 flute does not fit. I think someone said its a TYPE B wrench if you buy one at Pep Boys. Here is a link to buy a factory one:
http://www.finishlineperformance.com/store/product.php?productid=16839&cat=329&page=1
I was an idiot and thought I would take the filter cover off by hand. It is never going to happen, so I had to rush out and buy a typical band-type oil filter wrench and it sucked. Get the cup-style oil filter wrench.
Procedure: Warm engine for 10 or so minutes to get the oil warm
Jack up the car, put it on jack stands.
Remove under cover (10mm bolts, 1 philips screw)
Place container under drain plug (17mm) - Allow to drain - replace plug
Place container under filter housing - Use oil filter wrench and just loosen the Filter Housing Cover a bit - Like 1/8 of a turn - Use 6mm hex key to drain oil from filter. The reason to open the housing cover a bit is cause it allows the oil to drain out of the drain plug easier.
Remove filter housing cover
Replace O-rings (one on filter drain screw, one on black filter cover)
Insert new filter, reinstall filter cover to engine, re-install filter drain plug - If you like to torque things, torque values are on the plastic cover.
Pour in 5 qts of oil ... run engine for about a minute, check for leaks. turn off car.
Check dipstick level, and pour in oil accordingly. (Manual says with a new filter, car will take 6.0 US quarts) but, you must only add enough oil to get to the MAX mark.
Replace undercar cover, remove jackstands, and your done.