Since LTR implies trunking aka multiple frequencies in use on the same system then you're going to need to either decide to monitor them one at a time or install the Frequency Manager + Scanner plugin for SDR# to "scan" them (you add them, then create a group, and then you can scan the frequencies in that group). That's NOT the same as the somewhat limited frequency manager that's included with SDR# which basically just allows you to enter/catalog them and select them manually. First thing you have to learn about SDR# (and most any SDR program at this point) is it's not like having and using an actual scanner, even with that better plugin that allows you to basically jump through grouped frequencies, but it'll have to do for now till something better comes along in the future.
As for the National Weather Service, they broadcast Narrowband FM always so that's not AM at all. I use Blackman-Harris 7, 8000 for filter bandwidth for all NFM transmissions, filter order at 10 since I don't use it at all, squelch at about 60 for most everything (sometimes I'll push it to 75 on stronger signals so the squelch tail is shorter, I wish it becomes possible for someone to figure out how to get an audio processor of some kind into SDR# to cut the squelch tails down), and I have the Filter Audio box unchecked - I just leave it that way all the time.
That should at least be a decent basis for you. If you're stuck with the included tiny antenna you may consider getting a pigtail (MCX to BNC or whatever) so you can use a better antenna soon. The tiny one has given many people reason to attempt to get into SDR and then give up on it fast because they had a crappy first experience with using these RTL sticks and the main reason is because of the crappy antennas which are simply not up to the task of wideband monitoring.
And of course, don't forget about getting your ppm setting calibrated - choose a known frequency and then monitor it for 5-10 minutes, increase the gain on the signal a bit so that puts the tuner to work and warms it up a bit, then get the ppm amount adjusted dead on for the frequency so you're good to go. You may end up having to alter it depending on the band you're monitoring as well. Some people report that when monitoring stuff around VHF-Hi range it's one setting, when they move up to the 800 MHz range or higher they have to alter the ppm accordingly and so on. I have two sticks that when warmed up function with 50 and 56 ppm settings and I've rarely had to adjust them from those.
