In my experience, it's easier to deal with local movers completely separately from the shipping service. The one time I was on a time crunch and hired an "all-in-one" service, all they did was get local guys giving them the cheapest quote anyways.
When the movers showed up, they claimed they hadn't been told about "all the extra stuff" and quoted me literally double the price to pack it up. My wife and I had padded every number we gave to the moving company (e.g., room was 12' x 15' and we'd just say 15' x 15' and full of stuff) beforehand to avoid this, but they still tried to gouge us. I was able to negotiate them down by about 30%, but I was going to be on a plane in less than 24 hours; so they had me over a barrel. They would have been perfectly fine leaving me high and dry if I didn't shell out the cash either. It's an industry with a lot of predatory practices.
Meanwhile, every time I've just hired local guys on both sides and dealt with shipping separately, it's been cheaper (still not cheap), and I sleep better at night knowing that way less money is going into the pockets of middlemen.
I've had good experiences with ABF Freight, but it might not work for everyone. They drop off the back of a trailer at your place, let you load up, then you call them to pick up the trailer and tell them where it's going. They charge by the square foot of the trailer that you use, so there's some more savings there. They provide bulkheads that you use to seal off "your section" of stuff in the trailer, and they'll fill the rest with other stuff going to the same place.
Biggest downsides are that you need to have the space to put a 30+ foot long trailer (usually street parking unless your driveway is long and straight) for at least 2 days, and I would recommend that you have storage on the other side for your stuff even if you don't yet have a place because the one time that I had to pay their trailer storage fee, it was quite pricey. Also you gotta be flexible on delivery (don't pack anything you can't survive a month without) because occasionally, their drivers get rerouted or delayed.