The $350 price is pretty small.
The complete HTIB systems you can get for that amount are SO limited in connectivity and performance that they will frustrate rather than satisfy you. It is also junk that will end up in the trash eventually, and so will be a compete waste of money when you replace it.
I suggest that you get a decent receiver that will serve you for quite a while, and just start with 2 decent speakers.
You can do that for $350, and add a center speaker later, and then add a couple of satellite speakers.
I suggest that you get an Onkyo TX-NR 414 receiver, which is quite good and will last you for a while, for $199 at Amazon.
Then get a pair of Polk R150 speakers, which go for around $120 per pair.
Later, get the Polk CSR center speaker, for $65, and then the Polk RM7 speakers for $90 a pair.
You will end up with a system 200% better than any HTIB system you can get for under $600, and the total end cost will only be a bit over $450 total.