I think on such a machine as you have, the hp exceeds the machines stability to be used to its fullest extent. The reality is a 2 inch face mill with multiple inserts wouldn’t be any more advantageous than an old school fly cutter. Can it function, yes, but nowhere near its potential if you are only concerned about facing. A single point fly cutter can give an excellent finish at light depths, .005- .030 or so, and in a very wide cut.
Modern milling inserts and holders are designed to yield high removal rates, a lot of the design features preclude them from being used efficiently in low powered spindles that lack rigidity. This is accomplished with edge preps and geometry becoming more positive or tailored to materials along with various grades of carbide exhibiting toughness or wear resistance and enhanced coatings.
Productivity can be measured in cubic inches per minute of metal removal, on average it requires about .6 -.9 hp per cubic inch, a bit ambiguous because of the aforementioned tooling designs and efficiency. A decent 45 degree 2” face mill can comfortably remove 10 cubes a minute, 800 rpm, .200” doc, 1.5 wide @ .010 feed per tooth. My Excello 602 can do about 2 cubes per minute but nowhere near those parameters.
The 45 degree has the advantage of producing an average chip thickness of .007” at a feed rate of .010” so can be pushed quite hard, it requires a lot of power and good rigidity. Mostly the inserts available for thes style cutters have a heavier protected edge , a combination of chamfers and hones, at light feeds they are practically negative inserts, and need to exceed the width of the lands in feed rate to become truly effective.
The same with long-edge inserts such as the APKT style 90 degree cutters, they reduce cutting pressures through positive geometries, but require a bit mores rigidity as someone else pointed out, the opposing forces become radial rather than axial, pushing against the axis of the spindle rather than upwards into the spindle ,such as a 45 degree or a shallow cut on a button cutter.
The smaller diameter APKT styles can be effective though, 1” and under if you need to produce a square shoulder, as with anything it depends on the rigidity of your machine and the workpiece itself.
Because very few of us here are demanding money for our efforts we tend to ignore the time it takes , it’s a hobby or just the satisfaction of being able to do it. Trying to maximize removal rates is not compatible with the types of machines most of us have either, and we tend to spend our money a little more wiser where it counts and be resourceful in how we accomplish things with what we have.
Myself I tend to use a lot of carbide end mills, I would rather be milling at 1500rpm with a 1/2 cutter and getting through the work quickly than worrying away at 250 rpm with HSS, sure they are far more brittle than HSS but you get a feel for them, and typically the finish far exceeds what most indexable long edge inserts can give , and leaves a dead square face without steps. Dollar wise carbide is nearly as cheap as good quality HSS.
To answer a few more questions, the 90 degree TPU style inserts were acceptable in their day 30-40 years ago, there weren’t a lot of alternatives. They typically have a negative chamfered edge or more likely a rolled honed edge as well as neutral geometry presented to the work piece. They do suck up power and the lack of rigidity in the spindle or machine base itself shows very quickly and convincingly in chatter, an APKT style insert will outperform them in low power and less stable machines by a considerable margin, and they aren’t necessarily overpriced for the output they s give. A brand name such as Sandvik, Seco, Kennametal et Al will be $18-20 each for a 16 mm insert, likely $15 for a 10mm, the Amazon offshore ones are useable in a hobby environment and are reasonably priced. They are a better option than the old triangle neutral bodies and inserts.
Round inserts have their place for certain features, they can be ran shallow and at high feed rates with positive geometry and loads of edge prep options, they sacrifice surface finish somewhat when used as a face mill, they do not have wipe flats on the bottom as do square and AP style inserts. They will also push back and chatter on a light machine machine (such as the LC30 you have) if the depth is increased, not really a viable option for your machine.
A 45 degree cutter is useful in that it can chamfer as well as face but your machine (LC 30) can’t really use a 2” one to anywhere near its potential.
Get some decent carbide end mills, some small diameter HSS end mills for small key ways and such and find out what your machine is capable of and it’s limits, maybe borrow a 45 degree cutter and a Ap style and try pushing your machine a bit, the worse you can do is stall it, maybe chip an insert.