I suggest speaking with several lenders, the VA will have a list of qualified companies.
I do quite a few VA loans, and to answer your question closing costs would be no problem. The seller is allowed to pay all normal and customary closing costs, and is also allowed to contribute up to 4% of the appraised value towards other out of pocket items such as property taxes and insurance. With the furniture though you'd be on your own, unless you could convince the seller to leave some of those things.
I'd recommend scouting some estate sales or taking advantage of some 0% interest deals that are always offered by the furniture places.
There are other options that you may qualify for besides VA loans. For instance, USDA urban Development loans also allow 100 percent financing in some areas. I believe their website is