Is my receiver good enough?

Yes, it should do a decent job of driving most 8 ohm nominal speakers that are fairly efficient (sensitivity > 88 dB/W/m).

You're headed in the right direction - speakers will make the biggest difference in sound quality.
As long as your current AVR is handling the load I see no reason why it won't handle new speakers as well. Just make sure when adding new speakers you don't clip the amp - under powered amps are responsible for more blown speakers than high powered amps.

Your receiver can handle pretty much any speakers intended for use with a receiver with 8 ohm impedance.

Will it work better with some than others? Yes. Speakers with a higher sensitivity will play louder with less power. This is true of all receivers.

It comes down to power. If the 5930 was a budget model, you might gain better sound, through more power, at the midrange, such as the RX-V765.

My recenty created Yamaha platform thread explains this a bit better, showing where the tiers are. In each "tier", you get about the same level of performance; price differences are due to features (some model jumps are just silly in terms of how much you pay for what you get.)

I can't give you any speaker specific advice but here is the best advice you can get from anyone at any time: Go listen to the speakers you want to buy.

ONLY you can say whether you like the sound of any particular speakers. You know what your current speakers sound like, so only you can best audition any possible replacements.

And don't worry about whether they cost $1000 for a pair or $200 for a pair. This is the wild thing about speakers-- inexpensive ones can sound WAY better than expensive ones! Strange as it may sound, it is true and countless people who have gone through the process will tell you the exact same thing

Let me try to put it plainly.

There's a bunch of speakers made for receivers. The typical impedance is 8 ohms. While they vary in the power handling capability, and how easy they are to drive, they are all compatible with your receiver.

Some are easier to drive than others. Look for a spec called sensitivity. 90 dB is about par. Higher is better when considering how loud they will play. I suggest avoiding low sensitivity bookshelf speakers. For example, I consider 87 dB to be low*

* 87 dB does not make them bad, it just makes them harder to drive. You want to be able to play them loud enough for your needs without distortion, which I why I recommend more sensitive speakers

I started out basically the same as you only with a comparable Onkyo HTIB system. I upgraded speakers and the difference was substantial in all areas. Not only better sound quality which I expected but to my surprise the new speakers were much easier to drive due to the higher sensitivity. Most HTIB systems come with low quality speakers with low sensitivity and sometimes even 6ohm rating making them harder to drive. I found I didn't have to turn the volume up near as much to achieve the same db level with the upgraded speakers.

I'm not sure if you'll get the same results but in short as others have said as long as you stick with 8ohm speakers and a sensitivity rating around 90 or higher your receiver should have no issues whatsoever with them.

Jamo, Emo, Infinity Primus, Energy, TSC are other speaker options.

1. http://www.avsforum.com/avs-vb/showthread.php?t=1209191

2. http://www.avsforum.com/avs-vb/showp...postcount=6698

3. http://www.avsforum.com/avs-vb/showp...&postcount=252

Hello,
I would also add SVS's S Series Speakers. They are an amazing value and they are currently on sale. For 399 Dollars they sell a package with 5 speakers. One of which is a dedicated Center Channel. Also, for 799, they have a package with 5 of the SBS-01's and a PB-10 NSD Subwoofer.

The PB-10 is a legitimately good subwoofer regardless of price. As are the SBS-01's. The only thing you lose is the dedicated Center Channel, but you would have 5 truly matching speakers, which is ideal.
Cheers,
AD