What you're experiencing is alternator whine and there could be several reasons for that. It could be the RCA's themselves, if they are cheap and there is not much shielding or if shielding is poor, it will cause that.
The whine could also be because your power wire and RCA's are on the same side. Some people run their RCA's on the opposite side and it solves the problem, for others it doesnt, which means its more than like the RCA cable. When I had RCA's going from the front to the rear I ran them on the same side as the power and had no issues.
As for brands I really like Kicker since they are flexible and well shielded. They might be a bit pricier but it's worth it. Just check eBay. There is also KnuKonceptz, which several car audio goes with that I've noticed, but personally I like Kicker. I was going to use them, but instead I decided to make my own.
As for the loud thud or bump you hear, it could the one of two grounds. Make sure the headunit is grounded well to the chassis. Check the amplifier's ground. Rule of thumb is no longer than 3' ground, but the shorter the better. As for the ground, you want to make sure you scrape off any paint and you have direct metal to metal contact. Make sure the ground is secured by a washer and bolt and doesn't move around.
And not always is it the amplifiers fault. Sure you have a cheaper amplifier, but I have used the same ground for MANY different amplifiers. Used it on a DLS A6, A4, RF 500a2, Kicker zx 2500.1, rf t30001bd, soundstream xxx6500, alpine pdx 1.1000 and 4.150 (probably more that I cant think of). The only two I had a turn on thump was the zx 2500.1 and the t3000.1 (much more noticeable with the kicker). My recommendation is to turn the volume down all the way when you are done listening so when you turn the car back on, it will be minimal.