Randy,
I've been net control for the last three years down here in SW Oklahoma for the LIRA group. We have always recommended operators at least attend the spotter training put on by the Norman office every year, but we accept any and all reports from operators in the area or passing through (paging Daniel Shaw).
Over the last three years, it's become clear to me that there are two important factors in running a smooth severe weather net.
1. don't be too rigid, be flexible with reporting criteria, keep it open and inclusive
2. streamline your process of taking reports and relaying to NWS or what ever agencies you plan to serve
On point one, we always allow all operators in the area to check in to the net and participate. It doesn't seem like a good idea to require membership or a certain level of training in order to participate, because you never know ahead of time who might be in position to observe and report what they see. You also never know what chasers/spotters might be in the area for a big event. Those people can provide really great information and bring a ton of experience to the net. Having said that, over time you'll get an idea of which operators give reliable reports and can be counted on to provide accurate and relevant information. Our policy is to take all reports and then try to corroborate them against radar data, NWS guidance, spotter network data, other reports, etc... If it meets the NWS reporting criteria for the particular event, it matches the action in the area and we have some sense of the experience of the operator, we put the report into NWS chat. If it doesn't make sense or is not complete, we either filter it out, ask for more information or provide guidance to the operator on how to make better reports. Just always be respectful and helpful. Remember, most operators are just trying to help out and they don't know what they don't know.
One other note about being flexible about report criteria, if it's not a major event, we'll take everything from rain fall totals to structure reports and general weather nerdery. If there is potential for tornadoes in a storm in our area, we'll limit it to more traditional severe reporting criteria (hail 1" or better, 60MPH wind, wall clouds, funnels, etc...). Just be clear and communicate when it's game time and operators will understand.
On point two, practice, practice, practice. When there is a major event going on, the faster you can provide accurate information to NWS, the better. I wrote some software to make this process really fast for us and we practice with it every week by having a rag chew net. These nets keep my skills sharp, not only in operating the radio, but controlling traffic and recording information into the software. I try to get down as much of what the stations checking into the rag chew nets into our software as possible. This exercises the software and my brain as well as keeping a nice record of all the nets.
Speed and accuracy is the key. If you can get information about reporting stations ahead of time, do that and use it. We have a lot of operators that provide reports from home, we know where they are and confirm that when a net starts so that we don't have to get that information when they provide reports.
That's just a little advice I can give off the top of my head. Good luck!
-stephan kg5icz