You get an automatic free visa on a US passport when you enter Thailand. You can get a "visa authorization letter" online and then get a VOA (visa on arrival) at the airport when you land. There are two 3-month tourist visas, one for single-entry, another for multiple entry. The latter costs more. I used this site and paid $6 (Paypal) for the letter. The website said it would take several days, I think I got mine in less than 48 hours. When you get the letter, there will be a lot of other names. Make sure yours is on the letter and all your information is correct. It will help if you highlight your name so they can find it easily. It took a few minutes in line at the airport to hand in my application (you can download, print and fill out the application form at home, and attach a photo). Then you just wait while they process it. They'll call your name and it will also appear on an overhead screen with your photo. There's no real order, so people who came after you may get theirs before you. I waited about 15 minutes for mine. You have to pay cash (US$) on the spot. You don't need brand-new bills, but they should be in very good condition to avoid any problems. You can also go to a Vietnam Consulate/Embassy in the US - you may be able to do it all by mail - and avoid the wait at the airport, but it will probably cost more. If you were entering in HCMC, it might be worth it (huge airport, tons of tourists), but Hanoi is usually not busy and long waits are rare, I'm told. I went to Siem Reap in 2011 and got an e-visa on-line in advance. At the time, it was recommended because there could be long lines for on-arrival visas at the airport. As it turned out, there was a pretty short line. I haven't been to Laos.
My most recent trip ended just a month ago. My route was Hong Kong > Hanoi > HCMC > Chiang Mai > Bangkok. In Bangkok there are two airports. The main one BKK is easily accessible by public transportation (sky train). It's big - the biggest in Asia, I'm told. It's efficient, but be prepared for a long line for security/passport when you leave. Chiang Mai is small, no lines. I flew into SGN from Hanoi , so I don't know how long it will take you to get through the airport with an int'l flight. However, after baggage claim they were checking every piece of luggage against the claim checks, so be sure to have yours handy just in case. I had a checked bag on all the flights, which didn't seem to add much time, either at check in or at baggage claim. If you're going with just carry-on, be sure you know the limits - and remember the "liquids thing". It took up a lot of my time to do the packing because of the flights. . . . packing all the liquids so they wouldn't leak, arranging stuff so that nothing would get broken or damaged by the baggage handlers. And I really don't like airports and all hassle of going through security checks.
Be aware that HaLong Bay 2N will use up 3 full days. It's a long, slow drive to/from Hanoi. It's worth it. That was the best part of my 2 weeks in Vietnam. I mention this because you really don't have much time in Hanoi - just 2 full days at the beginning (jetlag???).
I don't remember waiting in line more than a very few minutes to enter any sights. I did spend a lot of time in lines at the airports, and a lot of time just hanging around waiting for flights to board. I flew JetStar from HKG and it was fine. I flew Vietjet from HAN to SGN and from SGN to CNX. The HAN-SGN was delayed by several hours with no explanations or information, including when they changed the gate but didn't post any info. They just turned off the overhead screen and walked away from the desk. Most waiting passengers didn't even notice. Also, all but one of your flights is int'l. That will add time getting through the airport on arrival. Also, it can take an hour to get to HAN or BKK or SGN from the center of town, depending on the time of day.