You’ve received some good advice so far. You probably already know that you cannot hike the Inca trail without a guide. Personally, I would have this guide arranged in advance, since you must reserve your entry tickets for Machu Picchu far in advance.
I’ve been researching a trip to Peru for some time, including reading lots of trip reports and talking with friends and family who have been there. You should know that if you do it (or even just parts of it) without a tour, it will involve some situations that may seem sketchy or make you uncomfortable. Taxi drivers hounding you at train stations, rickety buses, gross toilet situations (or lack there of). I’ve experienced all of the above in many locations, but it’s more prevalent in 3rd world countries. Depending on your views, and the views of everyone in your group, this can be an adventure or a nightmare experience.
My travel planning philosophy is to avoid the worst case scenario when possible. In this case, if you get your Machu Picchu tickets in advance but don’t arrange for a guide for the hike, what’s the worst that will happen? You’re stuck somewhere with no hotel reservations, no transportation reservations. Everybody looking at each other like “Now what?” And you could potentially miss your timed reservation for MP, which is probably the main reason for the trip. Maybe you’re fine living spontaneously, but that would stress me out and potentially waste a ton of money.
Will you be able to find a local guide once you get there? Yes. Will they be “official?” Maybe. Could they be a fake? Yes. Will they speak English? Probably. Will you run into someone who tries to rip you off? Quite possibly. Americans traveling in 3rd world countries attract attention. We are all seen as wealthy, and we are by the mere fact that we can travel half way around the world. That $10 you spend on lunch could be a week’s wages there, so don’t be surprised if you get some attention from locals offering their services, legit or not.
You mention hiking Laguna 69 and a bus going there in 8 hours. The bus goes to Huarez, where you would spend the night, do the hike the next day, spend the night in Huarez again, then 8 hour bus back to Lima. Then 2 more days in Lima and continue to Cusco. When planning an itinerary, I map it out by where I’m going to sleep, for example:
Day 1: sleep in Lima
Day 2: bus to Huarez
Day3: hike Laguna, sleep in Huarez
Day 4-5: sleep in Lima
Day 6-7: sleep in Cusco
Day 8-10: sleep on Inca trail
Day 9: Machu Picchu, sleep in?
Then I start filling in specifics for each day: where are you going to sleep, what are you going to do in specific days, when are you moving from place to place, how are you getting from place to place.
With a group of 6, I would make hotel reservations regardless of the time of year so you all get rooms at the same place. It’s hard enough to get 6 people out the door on any schedule, let alone if your spread out across multiple hotels with spotty WiFi.
I would look at booking.com for hotels. Then if you find one you like, check to see if they have their own website and (if you’re comfortable) book directly through them. You might save some $ booking directly, but booking.com provides some convenience and security that your payment is safe. Not fool-proof, of course. Again, it’s all about priorities: convenience/ cost/comfort level. Always choose the option to pay onsite in local currency, if possible. Get a credit card with no foreign transaction fees.
I agree with using a translation app on your phone. Have one person in your group designated as the one who pays to use data every day. I think Verizon is the most expensive plan and it’s $10/day. Then you can use all kinds of resources as you need them: alltrails, tripadvisor, translation apps, etc.