Wow, I respect anyone who does "Vegas on the Cheap". I wish I had the patience, but that’s why I’m trying to utilize this site and the valuable advice (my husband spends time researching, like you). Sounds like you have frugal Vegas figured out - nice to meet you.
Las Vegas Advice Forum is so well managed and friendly, I’m happy here!
The tentative plan:
When: September, 4-7 nights
Budget: mid-range, although I prefer higher quality accommodations. However, I also love coupons and a good deal!
Food: both fine dining & good buffets, minimal alcohol intake
Transportation: prefer walking or using the monorail (Several people I know used this to get around and liked it, your thoughts?)
Shows: Yes, Cirque du Soleil & open to additional suggestions
Attractions: We want to go to Hoover Dam and walk across the Colorado River Bridge, also go hiking & maybe biking (cycling) if rentals are available. The strip, etc.
Gambling: Novice, but definitely want to try and win 
My husband has not been to Vegas either, we are 35 years old and want to start travelling more. Vegas is our first stop!
Although a "virgin" Vegas visitor, (albeit with 35+ years casino gaming & gambling experience) I was definitely not a stranger to the world of casinos, the in and outs, getting comps, etc. I basically do not gamble, but am an advantage player. If I have an advantage, or even a perceived advantage, I am willing to wager, and won't balk at an amount. I will go to extremes to get the casino's money, including lies, cheats, or steals. I am a profitable poker player and spend more than 100 days/year in casinos somewhere.
I'm in my 60's barely, and a "single" hetero male. I'm also somewhat OCD, so am occasionally a little extreme looking for "deals". In 2009, my first Vegas "deal" was purchased through Orbitz, with a coupon from a Gay-Lesbian site for $100.00. It took me over a month to pull the trigger for a price, checking twice daily on all the travel sites, and discovering the best "deals" were Monday or Tuesday mornings. Result was something like $212.00 RT, non stop from Fort Lauderdale, including 6-7 nights at Binion's, with my return flight leaving Vegas at 11:00 PM and arriving home at 7:30 am. MY Vegas arrival was about 10:00 PM, and I finally got to Binion's by midnight on the shuttle.
I was unsure whether they would "check" if I was gay or not, but I was rather uncomfortable wearing that pink string thong. (OK, just kidding about the thong..... maybe.)
I was armed with several coupon books. And a load of extra coupons. By far the most profitable method to "win". Unfortunately, the quantity and quality of "good" coupons has shriveled to very little, and the +EV of the two main coupon books far from the values of 2009.
Over 55 days in Vegas in 2009, I played, used, and abused over 1,000 coupons. I chronicled my trip daily and in detail in reports on the "other" site. I visited more than 20 casino's in one day several times. I rarely spent more than 20-30 minutes in any of them initially. Just there for the "free money", than on to the next.
Since you are both "virgins", you should begin with a list of every casino. I recommend a spread sheet that lists every Vegas casino.
You will want to initially visit casinos with sign up bonuses for joining the player club. I would sign up, go to the nearest machine, play until I "qualified", use match plays if I had them, cash out and go to the next. As quickly as possible. I considered it work. A part time job, but I find/found fun in that. And in abusing the system by using more coupons than the terms and conditions stipulated, if I could get away with it.
I'm way more than serious, and 4-7 days is not enough time to "profit" and do the things you want to do. You could probably get between 20-30 sign up bonuses with free slot play from different casinos with coupons and promotions, plus a handful of match play coupons, etc. Even at warp speed, that does not leave much time for the other activities you'd like.
I used the bus, free shuttles, or walked almost exclusively. There is some debate among regulars about having a rental car to get from casino to casino. But if visiting "most" of them, IMO, walking and bus is faster because of parking. Not scientific, but I'd be happy to "race" anyone willing, with a minimum of 12 or more different casinos, within a reasonable geographic area. But again, I'm not skipping anything with "free money". I NEVER went on the monorail! Too expensive, when I had would get a 3 day bus pass.
I do not "do" shows. Instead, I opt for free entertainment, and IMO the best value is downtown. Fremont Street. And lower table game minimums, etc. There is always "something", especially in the evenings and at night. Concerts, sometimes shows, and more. I'd plan a minimum of two-three nights downtown, but than, I'd prefer to stay there also. It's usually more frugal, yet not necessarily lacking in "quality".
Always, and I mean always carry a bottle of water with you, and wear comfortable walking shoes. No one, except the person/people you are with will care what you look like, unless you're planning on hanging out at the clubs and high end joints. You should also have a hat, sunscreen, and outergarment during the day. Some places are downright cold after being outside.
Enough for now.
I suggest you read a lot of trip reports to help in your planning.
Good luck.
