I think its best to to buy a better, lesser expensiive gem, then a cheap more expensive stone.
Example $200 wont buy you too much in a sapphire, but it will buy a nice tourmaline or rhodolite garnet or zircon etc.
Green - chrome diopside is a nice stone - and untreated - you can get a nice one for under $200. If she likes apple green, you can get a nice peridot.
Pink - there are a lot of pink gems in the price range...all are treated though: kunzite, pink tourmaline, pink topaz (this one is really cheap, one step above cz in my opinion - and it is treated with diffusion - I don''t recommend it unless you''re really on a tight budget looking for a big stone). At $200 you can''t afford a nice pink sapphire.
Blue - hmmm. I don''t think $200 would get you much of a nice sapphire, unless you wanted a small one. Sapphire is my favorite blue stone. There are other blue stones, including the very affordable topaz - either treated by radiation for a swiss blue, london blue or sky blue color, or treated by diffusion for a "neptune garden" color.
I wouldn't say that, you can't afford a big one but you can afford a nice 1+ Ct pink sapphire with fine color (native cut of course, but not all native cuts are bad). Light to medium blue may also be possible.