Some ways are less expensive than others but there is no cheap way to get into techncial diving.
$300 for doubles rental in the course is a lot - as in the price of an entry level set of doubles. I recently paid $250 for a set of out of hydro 6061-T6 alloy AL 80's with bands and isolator manifold and with hydrotesting the total was right at $300.
For even less money you could also buy a set of travel bands and use your own tanks or rental AL 80's as independent doubles.
I agree you do not want your first dives with doubles to be in a class. At least a few dives will need to be devoted to getting the weight and trim adjusted as well as developing a comfort level with the new configuration. Attempting to do that in a course just creates enormous task loading issues and generally annoys everyone involved.
I also agree if you do not have access to doubles, you really should not be doing a deco diving (a possible but not ideal exception being a large 120-130 cu ft single with an H -valve) and the course makes no real sense.
In terms of progression, I'd get a set of doubles along with a BP and wing and get used to them within recreational limits. Some technical divers will object as they hold doubles to be a sacred part of technical diving, but it makes a lot more sense to be comfortable in them before taking technical classes. A course is not required to get to know doubles and the related configuration but having a mentor can help a lot.
Once that is out of the way proceed with Advanced Nitrox and Deco Procedures and go from there.
In terms of equipment you will ultimately need:
1. A backplate and harness.
2. A suitable wing for doubles. Lift in the 40-55 lb range usually works.
3. Two regulators for back gas. Both should be equal in performance and adeqate for air dives to 150'.
4. One regulator for your deco bottle. This does not have to be as high performing but bear in mind you will spend at least half the dive on your deco reg.
5. A deco bottle - an AL 40 or AL 30 will work.
6. DIN valves are not 100% required but are a really good idea.
7. A lift bag. A semi-closed cuircuit 75-100 lb lift bag with a pull dump offers the most flexibility. It can be inflated with a regulator, won't dump on the surface and can be used as a backup for buoyancy if your wing fails.
8. A suitable reel or finger spool. Spools are cheap, I'd get both.
O2 clean issues:
Your deco tank and valve need to be O2 clean and see only O2 compatible gasses- no exceptions ever.
The deco reg frankly just needs to be nitrox compatible. The whole O2 clean regulator required thing has in my opinion become badly overblown and taken to uneccesary extremes.
It is the tank valve that poses the major O2 threat and in particualar scuba valves as they tend to open very quickly and are not designed with flow passages that are O2 friendly and have much greater potential for producing an ignition source. In contrast almost any reg that is nitrox compatible will do fine with mixes over 40% up to and including 100% as long as you pressurize it slowly by turning the valve on slowly while the purge is slightly depressed.
O2 cleaning is a nice place to start and a good idea, but an O2 clean reg with 30 dives on it is no longer "02 clean" even if it has only seen O2 compatible gasses. None of them are "pure" they just have less hydrocarbon contaminants than non O2 compatible gasses and contaminants still have the potential to accumulate. Similarly, a deco reg that did a dive or two with non-O2 compatible air is probably still much cleaner than the O2 clean reg with 30 dives on it.
O2 cleaning is designed to reduce the amount of fuel available but an O2 fire will not occur without an ignition source even if your reg were soaked in gasoline, so your best defense against an accident is good operating practices designed to prevent rapid compression that could provide the ignition source.
In the interest of fuel reduction Nitrile/Buna-N o-rings are considered bad in an O2 regulator as they have a lower ingnition temp than viton or EPDM. They also theoretically degrade faster in 100% O2 but the difference is not an issue given the small total number of hours a reg will see 100% O2 exposure between annual services. Nitrile O-rings have been the standard in aircraft O2 systems for decades and degradation is not the issue it is made out to be in a regulator.
Viton and EPDM are more flame resistant, but Viton in particular does not hold up well in dynamic o-ring applications and is often to stiff to provide the same excellent performance that a nitrile O-ring offers. Using viton is just a case of getting a very slightly reduced risk of an O2 fire by paying for it with a greatly increased risk of a leak due to o-ring failure. It makes no sense.
EPDM is a better option as they hold up much better than viton in dynamic applications and do not impact reg performance like a viton o-ring may in some situations - but they are less flame resistant than viton. It is however all a matter of degree as just about anything will burn in a 100% o2 environment and a viton o-ring is going to burn just as readily as EDPM or Nitrile if its ignition temp is reached (and the difference is not that great) so the best approach is to ensure no igntion source is created.
EPDM and viton make sense in valve applications due to both the higher ignition temp and degradation isses given they are exposed 100% of the time to elevated O2 percentages - any dynamic movement against an o-ring in a valve is minimal. This applies to the valve on the deco tank with no exceptions, but may or may not be relevant to the manifold.
If all a manifold and set of doubles wil see are fills with banked gasses with no partial pressure blending using 02 or nitrox percentages over 40%, O2 cleaning is not required and the same applies to the tanks. Deep diving by definition involves low O2 percentages below 30% and often below 21% and if a fill involves putting a nitrox percentage under 40% on top of helium, there is no need for O2 clean tanks.
Some shops insist on O2 clean for everything other than air and if you are faced with that, you are stuck with O2 cleaning and related expenses if you want fills. There is some merit to only connecting O2 clean tanks to O2 clean systems as it would prevent contamination in the event you reverse the flow and introduce non 02 clean gasses into your system - but on the other hand that only happens due to operator stupidity and is preventable with a check valve. It is not always the shop's choice, often it is the insurance company that mandates it.