what's better free speed?

Hiring a coach has been hugely beneficial to me. The caveat that s/he has to give you something that is not stock, taking into account your particular strengths and weaknesses. 

I can't speak to your other options, but a good coach should be able to work with you regardless of the type of trainer or PM you have (not that having those things hurts). Good luck, and hopefully see you in Omaha!

I would do #3 over #1 as that gives you power both indoors and out.  I don't think any subtle changes to road feel will be worth very much.  The way to get used to riding hills outside is to ride hills outside.  

#2 has the potential to give you the most "free speed" in the sense that you will instantly (I use that term loosely) be faster.  There is no guarantee of course that this will really happen and it may not be a big improvement.  It very much depends on the position you are in now on your current bike vs what you end up with on the new bike.

2, 3 and 4 are the best choices in my opinion but there is nothing free about that.  

The highest bang for buck you mention is definitely the (good) coach, but that's with the big caveat that the coach is only as good as what you're willing and able to commit. If you want to PR, but you can only train -20% volume compared to your best season, or you consistently miss workouts in your coach's otherwise excellent plans, it's not the coach's fault why you're not PRing.

Road to TT bike improves you, but it's a pretty small gain. Better training will smash any aero gains in comparison. If you're that cash-strapped, you can skip the TT bike or even get shortie TT bars for your road bike. That said, everyone knows that rocking the sexy TT bike is one of the greatest joys of triathlon, and often THE greatest joy of triathlon, for many, so don't delude yourself into thinking your immune to bike envy.

The powermeter is actually not at all as proven at making you much faster. In fact, I'll bet that it won't make you significantly faster at all - you'll just have more consistent numbers to enjoy after your workouts. I used Virtualpower on Trainerroad for awhile, then upgraded to the TR+powermeter, with absolutely ZERO effect on the intensity and quality of my Trainreroad sessions (the numbers were different, but the pain was exactly the same.) The PM definitely helps for dialing in the small racing/training differences, but it's absolutely not guaranteed speed or training improvement, and actually doubtfully so for training since Virtualpower on Trainerroad works so well.

The smart trainer is also not needed, however if you're going to be realistically spending 4+ hrs/wk on it for months at a time, I think it's worth the investment. If you're <2hrs/wk on it though, save your cash. I went to the SmartTrainer, and it made riding indoors less mentally taxing, but again, the actual quality of my workout wasn't substantially different than non-Smart trainer since I was good about hitting power targets on the dumb trainer.

< 4min/hr in an Oly. A LOT less if we're comparing to a well-setup road bike with TT bars.

This AGer will likely get more than 4mins with better training/coaching. 

Myself and science in general are going to completely disagree with you on this.

I posted the below recently in another thread.  If you don't like that data feel free to play with numbers on BBS, Bike Calculator or whatever website or tool that quantifies it.  It's also not a mutually exclusive discussion.  You can train better and harder... and have a more aero bike.

Here is some data from Specialized from a few years ago.  There's probably more of a difference between the newer super tri bikes and road bikes but let's pretend that there isn't.  You can see there's a 3.5 km/h difference at the same watts from a standard roadie setup to a standard TT setup.  You can also see there's a 57 watt difference in holding the same 40 km/h speed between the two setups.  That's a lot.

Wind tunnel data

I've seen those numbers like hundreds of times. Even with those numbers, it's doubtful that an athlete will get more than 4 mins/hr of racing.

Here's an equally pseudoscientific article that I'm sure you've seen - they claim 122sec per hr saved with aerobars.

https://cyclingtips.com/2010/04/biggest-bang-for-your-buck-in-time-trial-equipment/

It'll likely be even less than that for most folks who don't hold the tight aero tuck for the whole hour, or aren't optimally fit with the aerobar tuck. 

For the OP, I'll bet a good coach and decent commitment will get him a lot more time gained than that. If he were a super experienced, KQ top AGer, I'd say otherwise, but sounds like OP is just getting rolling on the road to tri improvement, and I seriously doubt the road bike (or better yet, road bike + clip on aerobars) will be a significant limiter now.

*Shakes head*

Just getting in here because Chris is in here...

Since none of those are "free" what's your real budget.  Your list seems to be from a couple of hundred $ to maybe $2000, give or take.

1) I've had no issues with my KK trainer and hills.  I live on coastal FL and have to travel 70 miles to ride many short but steep hills of the FL peninsula ridge with out any problem.  When doing intervals on the trainer I mix up my gearing/cadence, I'm never static in a tight range.  I do threshold intervals between 60 rpms & 100 rpms. Hills require proper gearing to maintain an appropriate cadence range.  I setup my bike with 34/52 chainrings with a 12/25 cassette and can tackle anything here with it.  If I were going to real mountain areas the cassette would change to a 11 or 12/28 or higher.  One thing I do with my trainer is make sure I have a 12 sec coast down when I first get on (cold).  Spin up to ~20 mph and then get the approx. time for the wheel to stop.  This makes sure the resistance is the same setup to setup.  My bike mostly stays on the trainer and I do this every time.  From what was posted here on BT many years ago this cold coast down time should matchup well with the trainers speed power curve with a power meter.

2) Based on everything I've read and in above posts, a tribike with a good setup for you will be faster than a good road bike setup. If you can do that with a PM that's great.  But no need for a power meter if you are going to do virtual power on the trainer.  You'll correlate RPE and or HR to virtual power as I'm sure you have already.

3) That said, now that I have everything else covered from bike, helmet, training, etc., I'm in the market for a PM!

4) The right coach will be invaluable.  But I've read not so good aspects to due to bad coaches or the athlete not fully understanding the depth of coaching signed up for.  I've had great results just following a program off BT and tailoring it to my schedule and staying committed to it.