Most cross country moves require you pay per pound for moving. I got like 10 quotes when we moved from IL to NC, they varied from $2500 to $7000. I went with one of the most well known carriers and requested they weigh it as else its based on an "estimate" and I can tell you that estimate as about 1000 pounds too high (though I had purged purged purged).
I think it was roughly $40/100 pounds... so now you have to think whats worth moving. We paid for the extra insurance to cover replacement value not by weight since when you figure that out a $3k table may only net $300 by weight. I think my end costs was roughly $3400 moving what ended up being a nicely furnished 2 bedroom.
If we were going to move cross country again, I'd move the mattresses (as they are new and expensive), may grandmas antique table, and only minimal clothing and toss the rest. Even the TVs at this point are old, why bother spending money to box them when I can go buy something state of the art for a fraction of the cost.
We did put some of the super heavy items in the car we drove. Like my honey's weights, a good size toolbox, etc things that were 100s of pounds for relatively tiny items.
I thought in the end $3400 was a good deal, it included the movers at both ends, the drive across country and insurance and it all showed up the same day I arrived. By the time I would have paid for a Uhaul, help at both ends, gas, insurance, and the pain of having to tow my car and driving all that way in the uhaul thru the mountains, money well spent.
btw, it really depends on where in Texas as miles count too.. and Texas really is ridiculously huge.. had a friend move up Texas to Chicago, only when she told me the mileage to I really comprehend as she was down in McAllen (500 miles from McAllen to Dallas) and you haven't even left the state yet.