Bassoons are expensive ($3k+ for a decent student model)...I recommend renting the school's bassoon until late high school or until you know you are serious about playing long-term. Many school bassoons I've encountered are actually pretty decent, so as long as they are fully functional and you are playing in tune, I would hold off on purchasing.
If you are going to purchase, I recommend the Fox 222 or 220 (the 220 has more keys, but the 222 is good through high school). They both have a "long bore" design, which means they will have a stable, even pitch. If you want a more advanced bassoon without spending much more, get the Fox Model IV - it is resin but has all the keys you'll ever need. More expensive but excellent bassoon makers include Heckel, Mooseman, and Puchner.
Convenient bassoon features include the high D key, extra low C key, and a whisper key lock. Some bassoons have rollers between keys to ease finger movement. The Fox 51 model is designed to fit smaller hands. Click here to read about bassoon key options.
Where to Look Online for Used Bassoons: Midwest Musical Imports, Forrests Music
Bassoon Bocals Just as important as the instrument, the bocal greatly affects a bassoonist's tone. Fox bocals are always a solid choice, and the Fox CVX model is especially good for high notes. If you are able to spend a little more on a bocal, I recommend getting a Heckel or Puchner bocal. All bocals will come in a variety of lengths - #2 is standard. The higher the number, the lower the pitch, generally.
Good oboes are expensive ($2900 on the low end). The student brands I recommend are Fox (any model) and Yamaha (model 441). These oboes have good intonation, easy response, and are well-built. All models of Fox oboes have the Low B-flat and Left-F key, which are the two keys needed by high-school oboists for auditions.
Fox Models (ranked cheapest to most expensive)
333 - (335 wood version), modified conservatory system, plastic, has every key needed to play through high school and in community bands as an adult. The Yamaha 441 has the same key-work as this model, and is available in wood or plastic.
330 - almost full conservatory, plastic, moving from low B to low C# is slightly easier, low B-flat has a vent key to help its intonation. This is a good oboe for a student who is making District honorbands/All-State but will not be majoring in music down the road. It is a fine instrument for playing in adult community bands and orchestras.
300 - full-conservatory system, plastic
450 - full-conservatory with plastic top joint (to prevent cracking), wooden lower half. I took this one to All-State in high school.
400 - full-conservatory system, wood
Plastic vs. Wood: An oboe's tone has far more to do with the maker/brand than whether it is wood or plastic. Wooden oboes do have slightly better tone, but when comparing plastic and wooden Fox oboes, the difference is almost undetectable. Fox uses a heavy-weight resin that produces a beautiful wood-like sound. I have a plastic Fox English Horn, and I was unable to tell a difference in sound from the wooden version. For other brands, there may be more of an audible difference between plastic and wood. Wooden oboes are at risk for cracking, but this can be prevented with special care.
Be cautious of "big box" makers who also make other instruments - some these oboes can have severe intonation problems, thin/weak tone, and can be frustrating to play. If you see an oboe priced less than $1500, there is a good reason, and it will cost more in the long-run to either keep it repaired or replace it. Cross-check reviews on multiple sites (the IDRS forums and other oboe teachers' sites will have honest reviews). Learning the oboe is frustrating enough without having problems from the instrument itself. Never buy an oboe without a good return policy or trial period, and always talk to your private teacher first.
College music majors: Purchase a wooden, full-conservatory oboe. There are lots of makers to choose from, so come talk to me or your soon-to-be oboe professor when you are considering a professional instrument. I have a Loree AK bore oboe and a Fox English Horn.
Where to Look Online for Used Oboes: Midwest Musical Imports, Hannah's Oboes, Oboe Chicago, Charles Double Reed, Mcfarland Double Reed Shop, Forrests Music