You will have to search a LOT.
$400 for body, lens and a few backs seems pretty tight.
If you shop, you should be able to find something.
I think you could find a Speed Graphic with lens for your price.
I really doubt that you will find a Sinar + lens for that price. Consider a Toyo as a more affordable starter 4x5 camera. There are several other brands that are good starters, but I can't remember the names. Spend some time browsing through eBay, to get a feel of the brands and prices. That is what I did before I got my Toyo (on Craigslist).

As the guys suggested, think about what kind of view camera you want; press, field or rail. You can take rail camera into the field, but is NOT as convenient to do as a press or field camera.

Be patient and watch eBay and Craigslist, and maybe you might get lucky. I have seen great deals come up every once in a while, but you have to move FAST when you see a deal. I've seen "buy it now" deals scooped up soon after they were listed.

Also consider long term. If you get a GOOD lens, you can move that to a better camera (like a Sinar) later. So I would put more of the budget to the lens. On the other hand, you could consider getting a learning camera and get a complete camera (body+lens) in the form of a Speed Graphic. Not the best lens, but plenty adequate to learn on.