I've ridden to work for years, different routes (16, 3, 9, and 12 miles). The 16 mile route was mostly on a bike path, the others involved much more stop signs and red lights. With lots of stops the speed of your bike barely matters as the stops will make up a big percent of your commute (unless you run stop lights like a jerk, in which case you should stop acting like a jerk). Even without many stops you won't shave that much time with a fast bike. My 16 mile commute took around 70 minutes with a nearly 40 lb Fuji 10 speed from the 70s, but only went down to 60 minutes when I got a sweet 20 lb titanium bike from the 2000s. It was fun to pass people, but not life changing.
I've ridden lots of other bikes commuting over the years, a very new all carbon fiber bike an aluminum touring bike from the 80s, a fat tired mountain bike with rack, etc. After having done all that I think there are only 3 things that matter for a commuting bike.
1. Make sure you are comfortable riding the bike.
2. Make sure it can mount a rack.
3. Get the best value possible
For comfort try and find your size in CM and use that to base your CL search. Don't be afraid to search +/-3 cm from your size though as the size isn't always exact and different bodies. When looking for a bike I put "58cm", "58 cm", up through "64 cm" in the box find decent values and then actually ride a decent seaming bike for at least 10 minutes maybe even 20 to make sure it feels good before I buy it. The "size" of a bike is just a starting point, the real truth is in how it feels when you personally ride it.
You already seem set on a rack, but I'll re-emphasize for others reading: a commuting bike should have a rack. Riding with no rack and nothing to carry feels wonderful, but the reality is that your commute will eventually force you to carry things. Once you get a flat tire you'll realize you really want a pump and tire fixing tools; when you get frugal you'll realize that you want to bring your lunch to the office with you each day; some days you'll need to bring something home from the office with you. You could put these things in a backpack, but that's super uncomfortable in so many ways (hurt back, sweaty body, sweat touching stuff in your bag itself if it isn't waterproof). Putting stuff in a nice pannier on your rack is so much more comfortable (it is one of the reasons I sold my fancy carbon bike, cause it didn't have a rack mount).
Getting the best value bike definitely means getting it used on Craigslist. Since bikes hold their value well the true cost of a bike (that doesn't get stolen or destroyed) is really the missed investment of the purchase price and the price differential between when you bought it and when you sell it. This means that the absolute cheapest bike isn't always the best value bike to buy. I once bought a 4 year old $1600 bike, rode it for a year then resold it for $1800. I felt confident that I could resell it because it would have been around $3000 new and I saw similar bikes reselling for more in other parts of the country. I would not have spent so much up front if I had worries of theft though, but luckily I was able to keep the bike inside both my house and work and never have to leave it locked up outside. For bikes that I want to be able to lock up outside I generally keep the price under $400, but even at that price I still look for value and not total cheapness. At low prices value can be found more in things like newly replaced tires, chains that are in great condition, and shifters that work well. Also, don't use this advice to convince yourself that new is a good deal, bikes hold value well but still lose at least a hundred in value the moment the become used so you should always start used. Buying a $400 used bike that is currently in perfect working order and can be resold for $350 after a couple years of use is a better deal than a $200 bike that needs $100 put in to fix such things or a $600 brand new bike that you will only be able to resell for $400 in a couple years.