You could expect an initial earnest money deposit of approximately $1k to 1% of the sales price.
Home inspection should be approximately $300-400.
There is normally an appraisal cost on a purchase at the time it's done, but for a VA mortgage the veteran usually pays that as part of the closing costs instead of paying for it during the loan process.
Like has been pointed out, the closing costs will vary depending on the sales price of the home. In PA there is a 1% transfer tax per each side (buyer/seller) which makes your closing costs a little bit higher than average across the U.S. Also because VA loans require you to set up an escrow account to pay your property taxes/homeowners insurance into, the amount of property taxes will also play a part in how much your total costs are at closing.
On a $390k home in Feasterville awhile back the closing costs came out to $7k (including the 1% transfer tax) + the pre-paid/escrow account was another $7k, totaling $14k. In the actual city of Philadelphia on a $178k sales price the closing costs also came out to $7k (appears there was a 1% transfer tax per PA + another .5% per the city) + pre-paids/escrow account was another $3.5k (considerably lower property taxes), totaling $10.5k.
I can't speak for the market in Philadelphia right now, but in most parts of the U.S. it is still very much a buyers market and sellers are willing negotiate in order to make a deal, including paying some or all of the buyer's closing costs if that is what it takes. From the 10 years I've been doing mortgages it isn't too uncommon for the seller to pay up to 3% of the sales price towards the buyers costs, above that percentage there is usually more resistance, but it is all up for negotiation. If your real estate agent is saying that sellers do not pay closing costs/discourages you from asking for them, but that is what you want to do, then I'd continue to search for a real estate agent.