Okay, with active speakers, which was suggested by GranteedEV and not by me, the amplifier is built into the speakers. So you would connect the line level output of the TV (one of the pair of audio outputs on your TV) directly to the speaker inputs, which are not like the speaker inputs of passive (normal, unamplified) speakers. With active speakers, you would not need a receiver. This would be a 2 channel system, not 2.1, as there would be no subwoofer (the ".1" part).
With my suggestion, there would be a receiver (or integrated amplifier), which would be hooked up to your TV (same connections as above), and to the receiver would be hooked up passive (normal, unamplified) speakers via speaker wire. My suggestion would also be a 2 channel system, without a subwoofer.
Now, if you already have an Onkyo TX-SR308 receiver, you do not need to buy another receiver (and, of course, should tell us that you already have it when asking your initial question, as it is very important to the advice we would give). You can use it with most unpowered speakers, the exceptions being ones that have a very low impedance, or extremely inefficient (if you want high volumes).
With most receivers and most speakers, you can mix and match however you please, but you do need to be concerned particularly in cases of low impedance speakers. (And, in the case of powered speakers, which are rare among home audio speakers [as opposed to professional studio monitors, like the ones to which GranteedEV provided a link], one does not need an extra amplifier at all.) How low is "low" depends on the receiver or amplifier; look on the back near the speaker connections for the minimum impedance speakers that should be used with a particular receiver or amplifier, or look in the owner's manual. Most amplifiers are okay with 8 ohm or higher speakers, assuming that the speakers are honestly rated, and some are fine with lower impedance speakers. The impedance of a speaker is an electrical property of it, and it tells you absolutely nothing about how good it sounds.
Normally, it is best to pick your speakers first. Pick them by listening to a bunch of different speakers of different brands and different types, with music with which you are familiar, and then buy the ones you like best that are within your price range. You then select the receiver or amplifier, making sure that it is suitable for the impedance of the speakers.