I had the same issue as I have a single hdmi output amp (Sony STR-DA 2400ES). Did a lot of reading and spoke with others on this forum including some manufacturers e.g. Thatcable.com who were very helpful.
The things to understand is that whatever splitter/switcher you use including the one on board the amp the is some picture quality degradation. The question is will you ever notice it. I got hung up on the word splitter thinking it means split in half, I understand this isn't the case as boosters and circuitry reduce loss to a minimum.
I went for the ClimaxDigital which cost £29 and has a lot of good write up's behind it. It is also passive therefore no power is required to switch if your amp gives a power over the HDMI cable. If not, a a transformer power plug is included which also amplifies the signal. The switches from tvcables.co.uk or hdcable.co.uk also good as already mentioned but not tried one out. The point is £30 should do the trick. The matrix version whilst good, seems to lend itself better if you are to run two screens (say in different rooms) at the same time. The bottom line is expect to pay even more for this.
Also worth noting some splitters are poorer that others and can reduce signal quality over long distances therefore you might be sending a 1080p signal but only receive a downgraded signal to 720p as the unit can't handle it hence reviews are important to understand other people experiences.
That also goes for HDMI cables, I am running a 0.5m Chord to the switch, a 12.5m Van Den Hul hdmi cable to my Sanyo Z700 projector and a 2m QED-P HDMI to my 32" Hitachi UT32MH70. Whilst the cables are branded I never spend the earth on them, just looked around EBay. Van den cost just £26 the Chord £20 and the QED a mere £22. I am on the fence about better HDMI cables give better pictures but I do believe build quality is very important as I've bought cheap ones before that have failed or sent poor signals.
Overall really pleased with the result and a dammed sight better and cheaper than upgrading the amp. That's my view anyway.