ThatsDax: bicycle engine kit, bike engine, bicycle engine, bicycle motor
is one of the best for customer service I've ever heard of! I'd get my motor kit from him if I were you
Spooky Tooth: Spooky Tooth Cycles
and BikeBerry: Wholesale Beach Cruisers, Chopper, Mountain, Road, Tandem, BMX FreeStle and Bicycle Engine Kits - BikeBerry.com
are favorites of mine, they've treated me very
well. Dual start is... somewhat problematic as your pedals might not clear, but that can be fixed if ya need to. You can get a Walmart beach cruiser for about $80, quite a few on this forum have done so successfully.
There's this one for $84 that many have built and liked;
Walmart.com: Huffy 26" Men's Huffy Cranbrook Fashion Cruiser: Bikes, Scooters & Skates
but were I to get a cruiser, I'd be a bit more tempted by this one for $129;
Walmart.com: Schwinn Men's 26'' Delmar Cruiser: Bikes, Scooters & Skates
These engine kits do really well as just a single speed, the stock 44 tooth sprocket will do about 30mph once the engine is broken in and tuned, yet still has enough pull for a trailer. There's no real need
to get a multispeed bike, you won't be pedaling except to start the engine and to be nice to your clutch on take-offs from a dead stop.
There's a great jackshaft kit from Sick Bike Parts LLC - Performance Parts for Your Motorized Bicycle
to have your engine utilize the bicycle's gearing - but it's somewhat expensive, don't really need it, and although it's great - it's mostly a performance mod/upgrade. I would however very much recommend Jim's sprocket adapter from MANIC Mechanic Parts.htm
as it's inexpensive and solves the biggest problem with these kits - the rubber mounted rear sprocket.
2-wheeled passenger trailers are so common used (and cheap) it's nuts, I'd try Craigslist craigslist: new york city classifieds for jobs, apartments, personals, for sale, services, community, and events
or your local equivalent (classifieds), prolly can get one for less than $50. There's quite a few people with trailers for their bikes around here, bet a few haul kids w/em - I'd just not have the cover/roof on it on the remote chance exhaust fumes could build up.
You should be able to get all of the above (except the 7speed/gears) for about $300 or so, including a used trailer - less if you're resourceful.
Welcome to the forum BTW