Should I use a passive or an active filter?
In traditional radio, pretty much all the filters are passive because historically, none of the amplifying devices had enough gain-bandwidth for a satisfactory active filter. So active filters here are a departure from tradition - but with high speed opamps, possibly a feasible one.

In any case, any filter before the first amplifier has to be passive by definition! You can combine a passive filter with an amplifier stage - i.e. a tuned load. Active filters tend to have higher noise levels, so best not applied to low level signals.

Also note that - answering LvW's comment about a Q of 108 - filters ahead of the mixer are usually relatively wide bandwidth, determined by whatever Q you can economically achieve.  Most filtering happens after the mixer, at the (generally lower) Intermediate Frequency (IF) - traditionally 455-470 kHz.. 

Because the local oscillator is tuned, the IF is constant so the narrow bandwidth (10kHz in your case) is a fixed filter. And because the IF is usually a lower frequency, the Q and GBW required are lower. 

So you could employ passive filtering at RF, and a fixed frequency high order filter at IF, and nowadays the latter could be either passive or active.

For completeness, some radio systems use a high IF, perhaps 10.7 MHz, with extremely high-Q (passive!) filters made using quartz crystals as bandpass filter elements instead of their normal role in oscillators. Some also use more that one IF - a first IF at 10.7 MHz and a second at the traditional 455kHz.