I am thankful to watertreader for posting this question as I am wondering the same question.
Both Halls and Laktronics had provided very good points on the benefits of having the amplification first and having the filtering first respectively.
According to this video below, the band pass filter after the LNA combination really made A LOT of difference to an analog 1.2ghz video's reception :razz:
https://www.youtube.com/watch?v=-KIT70vCoiI
I planned to use an LNA to enhance 5.8ghz reception of my drone's video transmission and had ordered an expensive 50usd "gpiolabs" 6ghz LNA (0.8db NF) and a cheap 10usd "Aliexpress" 6ghz LNA (4.5db NF). Both appear to have a gain of 15db at 6ghz.
The Aliexpress one appears to be using the Mouser SBB-4082S IC (or equilvalent IC) while the gpiolabs one is using a better IC which is concealed by the aluminium shielding case. I am not even sure if a BPF is necessary for 5.8ghz analog video or for 5.8ghz digital HD video. As proven in the youtube video above, LNA + BPF appeared to have an improvement when a low gain omni was used on the receiver and it had little effect when a high-gain directional yagi was used on the receiver, which is kinda interesting.