I'm learning oud since 5 months now. I don't have any experience with banjo, but sitar (from Indian Classical Music).
To address your questions, in my opinion, oud is a bit easier than sitar, but probably more difficult than other instruments, specifically for getting the right intonation (and we're speaking microtonally). As always, the more you practice, the easier it gets. I made more progress with oud in this 5 months than what I could with sitar in the same amount of time, but that's still relative.
On the other hand I would say a $300 dollars oud is pretty cheap, so I would say it could work fine. Regular ouds are around $1500 dollars and more too. Someone mentioned a $50 dollar oud in Egypt, but beware decoration instruments sold in fairs or souvenir shops (they exist in India too and sell very decorative but otherwise "firewood" sitars). Who knows, maybe you do get a decent cheap instrument by a young, starter maker, but be very careful.
With regards with what you should look in a starter oud, I would say that the highest quality, the less problems you'll have tuning it, etc. But that doesn't comes with a starter price. On the other hand, since I wouldn't recommend learning on your own since you need to know the position (specially right hand/arm), the technique is very different to other instruments, and the music itself is very complex, you better try to find a good teacher and ask him the type of oud he recommends. There are ouds from Iran, Iraq, Syria, Egypt, Turkey, and so on, and many of them are different with regards to size, stringing/tuning, sound, etc. I would say the most different is turkish with regards to the others, because not only tuning is different, but construction is very different too (and thus, sound). Then, your teacher can recommend you also a place in the US for you to buy one. Buying overseas is pretty delicate and you have to know more or less where you're buying and what you'll most probably get.
As someone also posted, Mike's Ouds Forums is a great resource and can help in many regards.