Welcome to the forum dawrock!
I'm going to take your questions in reverse order.
It probably makes sense to start locally. I started doing the travel mystery shops at hotels and such AFTER I already had some experience mystery shopping and doing the more normal evaluations of banks, gas stations, grocery stores, fast food, restaurants, etc. There are enough companies that want you to have a track record before you get ANY work from them, that getting started where you can, doing what you can makes sense.
Shopper preferences for companies vary greatly. I like some companies that others dislike vehemently because I rarely have issues with them while others do and vice versa. It may be the schedulers or editors for the particular areas or jobs, or it may just be that their jobs are a more or less intuitive match for me. There is a list of legitimate companies in the first thread of the Mystery Shopping Company Discussion thread. This is not a complete list of companies by any means, but it is probably a good starting point.
In terms of 'shopper organizations', there really aren't any. The closest you will find is the forums. Other that company owned/operated ones, this one and the one at Volition.com are the only open ones even relatively active that I know of at this time.
Some shoppers feel that buying certifications from the MSPA give them a leg up on getting work, and you can find the discussions on this forum with a search of 'Gold certification' readily enough.
I would suggest that you talk with your married couple friends about what they are doing, who they are doing it for and ask for a referral once you have been shopping locally for a while. Due to rotation as well as some of the travel shops being for singles while some are for couples, you would not likely be direct competition taking dinner off their table.
When I was doing such shops it was through Freeman. I haven't done them in several years and at least on the shops advertised to the general shopper population, they are running months behind on payments. While I was doing them the biggest issue was the time/lack of time involved. There is little glamor in spending 8 hours travelling to a location, the next 20 hours observing everything from baseboards to valet service, trying every restaurant and service of the location, causing interactions with every department and writing up lengthy questionnaires and narrative, to have everything except the final checkout experience done when you check out and spend 8 hours travelling home. Yes, you just went to Timbuktu, but you only saw it as you drove/were driven out to the hotel and through the windows of the hotel.