This answer will confine itself only to the size of the conduit you should lay, and as you'll soon see, even such a simple question has layers of complexity.
This work will surely need to be fully permitted and that means it will need to be done to the spec of your AHJ (generic term for your electrical inspector: Authority Having Jurisdiction.) That will be the reason for the engineering review.
Metering and fusing at the supply
The other company certainly isn't going to give you 30kw of power for free. There will need to be a metering arrangement at that site, whether that's submetered and rebilled by the other company, or the utility puts a meter there.
There must also be overcurrent protection for the long run from this supply transformer to your site. This may not be a simple household style "breaker box" as you say.
This stuff all needs to be figured out before you can really advance further. What you can do is get the conduit laid in the ground. Conduit is mandatory, which means cable is impractical. Into the conduit will go several single-conductor wires, of a rating fit for outdoor/wet location use, such as THWN-2.
There are a variety of conduit types, such as PVC plastic, EMT metal, IMC metal, or the heaviest Rigid metal. Rigid is pipefitted, with screw-in fittings. All conduit is presumed to be full of water at all times. The defense against water is in careful selection of wire.
You may have a maximum of four 90 degree bends (or rather, 360 degrees total) of bends. However even this will be quite tough to pull, and will require a professional with his truck full of special pulling gear. It's best to keep bends to an absolute minimum for ease of pulling, but typically you need two 90s just to enter and exit the ground.
Trenching depth is a big deal in some cases. Rigid conduit (the most expensive) needs only 6" of cover atop it; 12" if it's under a driveway or parking lot. Other conduit needs 18-24" of cover.
Figuring out conduit size is pretty simple, the conduit size is decided based on the number of wires and the size of those wires. Look it up in this table or this calculator and you're done. Easy peasy
Wait. How many wires?
First, metallic conduit can often be a grounding path, in which case a ground wire is not required. I am skeptical of metal conduit outdoors being an effective grounding path if it isn't Rigid conduit. You really want a ground wire, so don't mess around here. If you need a ground wire, it's allowed to be smaller than the conductors.
Ground aside, the number of conductors depends on the configuration: 3-phase "delta" or "wye". Delta has 3 conductors and no neutral. Wye has 4 conductors and a neutral. Most motors do not use the neutral. In most cases the neutral can be downsized when the loads are expected to be balanced (which motors will be).
A wye supply can drive delta tools. In some cases, if the supply is wye, and you only need delta, you can simply take the 3 wires of delta.
This brings us to 3, 4 or 5 wires.
How large should the wires be?
You want to size your conduit for the worst-case wire size that you might ever need. Conduit is more expensive than wire when you account for installing the conduit, repaving and the like.
You have provided a power requirement (120hp machine under test + 40hp compressor that someone will someday forget to turn off while testing). That's 160hp or roughly 120kw.
You don't have a choice whether you'll be getting 208V, 240V or 480V, unless you intend to provision your own transformers.
Running the numbers for 480V... 120,000 watts divided by 480 divided by sqrt(3) = 144 amps. That's enough infomation to head over to the Voltage Drop Calculator, using 5% as the tolerable voltage drop. We get less than 2% drop with 1/0 Copper wire, which is a better answer than I was expecting. 480V really is magical stuff.
At 240V it's a bit more frightful: 289 amps. Calc says 350kcmil copper wire - yikes. "Kcmil" aka "MCM" is for large size wires too large for the AWG sizing system. At these large sizes, you should really have a talk with the AHJ about using aluminum. Copper is not for this.
At 208V, we're talking 333 amps. Calc says 500kcmil.
Trying to run a 120hp machine on anything less than 480V 3-phase seems like madness.
Back to conduit size
In the 480V case (#1/0 wire), you could skin by with 1-1/2" conduit, but I would upsize to 2" instead, for ease of pull and future expansion.
240V (350kcmil) could get away with 2-1/2" conduit but I would go 3". 208V (500kcmil) will require 3" conduit.
There's no penalty for installing too-large conduit, except the cost of the conduit itself, which is negligible in the scope of total project cost.
Fitting conduit is a huge amount of the total work, which is why it's a good thing to DIY. That done, pulling the particular wires required is straightforward work for your electrician when she has determined the right wire size.
There's also no penalty for installing too-large wire (except for the cost of the wire) however expect that cost to be considerable.
Adapting your machines
480V machines can often be re-jumpered 240V, or vice versa. There will be a label on the motor indicating how to change jumpers. It's not hard to design a motor to be 240/480, just not every motor is.
Some 240V machines can be run on 208V, or vice versa, but it's not as common. Thermal machines like ovens will produce less power (208/240)^2 - and motors would need to specifically be designed to be dual voltage 208/240. You have to consult the documentation.
If you need a voltage you do not have, you will need to provision either a 3-phase transformer, or three single-phase transformers connected correctly. You could have them right in your shop.