Great choice, bassoon!
Personally I would rent / buy second hand. Renting for the first 2 terms is usually a good first step until you know if the child is going to continue with the instrument.
There are plenty of second hand instruments around - look at notices in the local music shop, or ask their teacher; there are lots of people who buy new and then the child gives up and you can get quite a bargain. Also look at online 2nd hand sites. You can then pick up an instrument for a fraction or the cost. But you do need to know what you are buying; ask the music teacher to write you a spec before you start looking / show them adverts you have seen and ask their advice.
By the time you know you want to stick with an instrument you then know what would suit youâ€¦.the difference in quality between a cheapish second hand one and something decent really doesnâ€™t start to matter until you are at least grade 6 or above. The ability / interest of the child and the quality of the teacher is what makes the difference! There are also enough other costs incurred buying music.
If a child is really gifted, there are schemes for loan of quality instruments at nominal charge. Have a look at this link â€“ it gives many of the schemes around and links to various loan options. www.a-y-m.org.uk/links.html
It includes a link to the arts council scheme called â€œTake it Awayâ€