I have a Sony PDX10, and want to upgrade the sound capabilities. I am going to shoot a documentary with interviews both inside and following my subject on the streets(run and gun). I will work alone so no booming is possible. This is my suggestion for mic setup based on what I have read on other posts.

1)
One Azden SGM-1X Link (http://www.bhphotovideo.com/bnh/controller/home?O=productlist&A=details&Q=&sku=238826&is=REG) . Shotgun which replaces the standard NV1 shotgun on camera. Records to channel 1 XLR. I have also read a lot of praise regarding the Audio-Technica AT897 Link (http://www.bhphotovideo.com/bnh/controller/home?O=Recommend&A=getItemDetail&Q=&sku=300615&is=REG), however it is more expensive and I think it would rather spend more of my budget on the wireless lav kit.(see Samson below).

2)
A wireless lavalier which I record on channel 2 XLR. I go wireless since that will make me a lot more confident getting good sound on a moving subject. I am considering the Samson Airline Series (UHF) Link (http://www.bhphotovideo.com/bnh/controller/home?O=productlist&A=details&Q=&sku=219777&is=REG). As I understand UHF is less prone to interference, and when shooting on the streets of New York I suppose UHF is better than VHF(for instance Azden WLX-PRO Link (http://www.bhphotovideo.com/bnh/controller/home?O=productlist&A=details&Q=&sku=3656&is=REG).). I will also get a Rycote windshield for the lav.


My goal with this setup is that the shotgun on camera and lav combined give a good recording of the subject´s voice as well as ambient sound. However I am not sure if a shotgun type mic best compliments the lav. Will it be better to use a more omnidirectional mic mounted on camera since my subject already wears the lav? I am worried that the standard NV1 is actually better than a shotgun?

I have no previous sound recording experience so if anyone has a comment it would be greatly appreciated!

The stock mic on the PDX-10 isn't bad as stock mics go. I think it would be equal or better than the SGM-1X.
I'd say put that money into a wireless with a broader frequency selection. NYC is going to be prone to interference regardless, so having a wider band of built-in frequencies to choose from would be a great benefit.

So maybe I should invest in a system like this then, and leave the NV1 on camera :
Samson Micro 32 Series Link (http://www.bhphotovideo.com/bnh/controller/home?O=productlist&A=details&Q=&sku=187777&is=REG) then I have 32 channels.

Or is there another wireless kit that does a better job at no more than 350 USD?

I don't know of anything better in multi-frequency UHF at the $350 price point. The Sennheiser G2 100 series at $500 works well and has a very broad frequency selection plus the ability to scan for clear frequencies. You'll definitely want to work with a TV channel frequency chart and the guys at B&H when you pick your system. NYC is very crowded. See this list from Sennheiser for all of New York State. Look at the greater NYC area.

http://www.sennheiserusa.com/newsite/mat_dev/frequencyfinder/PDFs/NEWYORKew.PDF

Is the stock microphone on the pd150 the same as the microphone on the pdx 10? I am in the same boat (actually I just ordered by wireless system) -- and was now wondering wondering whether I should keep the stock microphone (and spend my money on something else) or switch it out for something better.

Thanks,
Albert

I don't know about the older 150, but the 170 comes with the NV-1.
When I compared the sound between the NV-1 from the PDX-10 and the stock mic on my DSR-390 that was ordered at the same time, the sound was indistinguishable. Physically they are the same except the NV-1 has a plastic body and the mic on the 390 has a metal body and no model number that I could find. Your 150 mic is likely very similar.
Replacing it would be up to your budget and what you need to accomplish. The AT4073a is an excellent mic and has a hot output that can help the 150 considerably. For strictly camera-mounted use in run and gun situations, it might not be worth the expenditure unless you're already unsatisfied with your current results. The Sennheiser K6/ME66 is also a possibility, but there are plenty of situations where it doesn't perform well and it's a far cry from the performance of the 4073a.
The AT897 is an excellent mic, but its moderate sensitivity doesn't help the 150 unless you're constantly in loud ambient sound situations.