That's a really good question. There are so many amps out there that don't perform to their stated rating.
The first awesome amps that I think about that are fairly priced are Emotiva.
BUT, this question is in the "Car Electronics" category, so I'm assuming that this needs to be for a vehicle... and you confirm that by saying what your vehicle fits. I was hoping to turn you on to Emotiva, but that won't work for the car.
Based on your concern for the output power, what we need to look at is RMS power and not Peak power. Most amps will advertise Peak power, which isn't very meaningful. RMS power is the power that the amp can maintain continuously. And IMO, is a better measure of what the amp is. A manufacturer can make an amp peak at just about any power just by making the reset of the amp suck more. Sorry if I go on too long about this, but buying stuff like this is one of my favorite things to do. Here are my recommendations. These are not necessarily in order of preference - they will ALL do at least what you are asking, they are ALL excellent, no BS amps... very capable. They may be different in their approach, but any one of them would be a good choice.
JL Audio makes a 4 channel amp. Actually they make a few, but this little powerhouse is well within your price range and puts out 150w RMS with 4 channels:
That would pair nicely with their monoblock 600 1v3 for the subs:
Those are pretty high end - but right in your price range. On the lower end, but still very capable (one of the few "less expensive" brands I would use myself)... Rockford Fosgate Prime series. Example: This one amp will give you 50 Watts x 4 + 200 Watts x 1 @ 4-Ohm / 75 Watt x 4 + 300 Watts x 1 @ 2-Ohm. Not exactly what you are asking for in terms of power for the four main channels, but it is RMS and the whole thing will only set you back around $225.
Another amplified in this class worth mentioning is the Kenwood X700-5 - 700W 5-Channel Amp. This series by Kenwood has the smallest footprint of all the amps in this class (other than their RX "Reference Design Series), so if you are tight on space, it's a great choice. And it's RMS Power Rating is as follows: 4 ohms: 40 watts x 4 chan. + 300 watts x 1 chan. 2 ohms: 50 watts x 4 chan. + 500 watts x 1 chan. Bridged, 4 ohms: 100 watts x 2 chan. + 500 watts x 1 chan. It's definitely one of the best amps in this range. It has excellent sound and no distortion.
Another amp that you should take a look at is the Alpine PDX. It's a Class-D amp on a small, 2” tall frame. It's still very effective at heat dissipation, and the sound is superb. One thing I love about this amp is the special connectors it has - they pop out which makes installing and removing the amp EXTREMELY easy. The PDXF6 / PDX-F6 / PDX-F6 4 Channel 150W puts out 150W x 4-Chan. @ 4 ohms. It's one of the best amps you can get in this price range.
I'll stop there. But if you have any questions, or if there are other models you are looking at, let me know and I'll be happy to continue the conversation.