Okay here is the deal, you can get H&R springs for the 2010 Mazda 3. But in actuallity, you can get any spring you want since they are all the same from Gen1 to Gen2. I just put gen1 MZ3 springs on my Gen2 MS3. Anyways, you can go with just springs for a slight drop. Or you can go with full coilovers for a slam. But with the coilovers you can adjust the ride height and dampening on most models. So you can pick and choose exactly how you want it to ride.
Springs:Most springs are going to cost you $200-$300. Using only springs will wear out your stock/oem struts quicker and the ride might be a little more rouch on heavy bumps since the strut will not have as far to travel.
Shocks/Struts:Just the shocks/struts are going to cost you $450-600. These will have to be purchased along with springs. But choosing them seperately will allow you to customize exactly what you are looking for. But if you dont know exactly what you want. Be weary.
Coilovers Coilovers will run you $900-$2500 These are your best bet, but cost the most. They are well worth the money, especially if you want to have some spirited driving now and then.
I would say if you can afford it get the BC coils. They are great from what I hear.
For guidance on doing the install. If you dont have the know how. This would be a great way to get to know your car. So ask some local people to help. Or you can pay out the butt for a pro to do it.