Since your gain requirement is pretty high, I'd do it in two stages or more, 50MHz GBP gets you 20dB of gain at 500kHz, so trying to do it in a single amp means you need an absurd GBP, but doing it in two stages you can find some reasonable amps for, and doing it in 3-4 stages will get you a lot more options in terms of inexpensive low noise amps. Something like a 3 stage amplifier would let you use 8MHz GBP opamps, for which low noise variants can be had reasonably inexpensively, with 12dB of gain at each stage, in fact, you could just look for decent quality audio opamps and use them. The trickier part is the 3V supply, but there are plenty of options given the popularity of those lower voltages in mobile and low voltage devices, so find at least 9.5V/us slew rate or so if you need a full scale output and look for something rail-to-rail to utilize it fully and use at least 2 stages to do your amplification.
If you really need that 35dB to happen in a single stage, something like a MMIC is a much better choice, but a small 8 pin TSSOP with two opamp elements and a few passives wouldn't be enormous and should do the job reasonably.
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