You’re going to need to adjust your expectations in my opinion.
You cannot use a mountain bike, - it will be so slow, - you’ll get killed.
I agree that you need an entry level road bike. Entry level road bikes start at $1000 at the lowest.
This will be unfair to a local bike shop, - but if you’re really on a budget, - maybe you can go back to them later and make good: but, I would go to a local bike shop, take a look at an entry level Bianchi, and an entry lever trek or cannondale. Get them to get a ballpark sizing. For example, if your 5’10" a close/ballpark framesize on a bianchi is around a 55 or 56 cm. Ride it and then ride a Trek the same size to see if you like Campagnolo or Shimano components, - both are good, - just check personal preference of how you like to use the controls.
Then look for your fav one of those bikes used… (late model).
If you score, - then take it to a pro fitter, - preferably someone who does Serotta system or someone of that ilk.
As most people say here, - you can’t emphasize the importance of fit. a Fit brings you optimum power and comfort on the bike, - which is ABSOLUTELY CRITICAL. It’s better to buy a $1000 bike and get a $500 fit than it is to buy a $1500 bike. Many places that will sell you a good bike on sale, don’t know crap about fitting.
I spent $400 on my fit that lasted 6 hours and it was totally worth it. If someone spends 1/2 hour fitting you, - it will be bad…My fit guy spent nearly an hour on my feet alone… Plus, during the fit, - unfortunately, - you have to count on spending more money on parts, - like stems, to do something like bring your handlebars closer or farther away or whatever…
When all that is done, - you’ll need to go out and buy yourself a good set of clamp on aerobars, - hopefully during the fit.
I can’t say enough about how much faster you are going to go when you’re in a stable aero bar position…
Go out to Google and do searches, and check the FAQs to see all of the great advice on Time Trialing, and Time Trialing bikes and the importance of the streamline position…
This really isn’t esoteric stuff, - it’s important to start off at least close to being correct, - otherwise, - you’ll be throwing money away AND not getting the right first impression that you’ll need to even decide if you like it, - let alone keep up.
If you use a mountain bike with slicks, you’ll not have a good first impression, and it is very likely that you’ll end up not doing the sport, - that’s how much it’ll affect the experience, - seriously.
Plus, riding a roadbike takes practice, and then a LOT MORE PRACTICE riding in aero bars. Believe me, until you get the hang of it, - the bike is crazy out of control riding in aerobars, - you need to get used to them… but first things first…
You may be able to find a Bianchi Eros, or a Veloce, or a Giro used for under 1,000, or a nice Trek or Cannondale. Get a decent fit for $400 and a pair of aerobars for a $100… and count on spending $100 on shoes, and hopefully the person will sell you their pedals too…
You should expect to be paying $1500 to get you in a position to get a first impression…
You can buy that $7000 Pinarello TT bike a few years down the road…