Weight as listed is 6,090 lbs. A car hauler capable of handling a 10,000 load is what I have used to move up to 8,000 lbs. Should have a metal deck, and you will need proper rigging. This means chains from the back, straps from the front. That's a mistake I see everywhere, from people moving riding lawnmowers, to just junk on a trailer. The use chains on the front, and a comealong on the back. That's exactly backwards. Since the most abrupt change in forces would probably be a front collision, the load will want to shift forward. So it makes sense to use the most secure anchor method from the back. A chain, no boomers (load binders, etc.) at all. Just a chain shortened up to where it needs to be. Then all the securing force should come from the front and sides. The front primarily because you are most unlikely to out accelerate the load and cause it to shift backwards, and the odds of someone hitting you from the back are minimal, given you will have reduced braking and the following vehicle should be a friend in an escort vehicle keeping some safe distance and watching for your braking anyway. So your ratchet straps, boomers, comealongs.....etc, all should come from the direction you will be pulling against the strong link.....the rear chain. I live in oilfield country, as well as timber hauling country. I have loaded out many tons of material and equipment. I also have observed the way and why things are done a particular way. Think through the forces involved in a static position, then imagine all the dynamics as they possibly could come into play in different situations. It pays to think of the impossible. And then prepare for it. If you do that, you should have a boring, uneventful ride. Then the nerves come into play as you work to pick and place the load. Think ahead....never behind and wish you had done things different. People get killed too often by not thinking ahead.
For this load, a 10k forklift would be my choice, but only if it will fit in the building. It can be surprising how small some warehouse tired lifts can be and yet be rated very high. Don't let the size fool you. Go by the ratings. If necessary, that machine could be lowered onto skates and pushed/pulled into position with a smaller lift, if you can't get a small heavy lift machine. Bear in mind also that a standard garage floor isn't designed for this load. It's common enough to consider cutting out a section of your current floor and pouring something a bit heavier. You would be better off doing that than dealing with a broken slab later.
There's much to be considered when you move up to this class of machine. I have no idea of what you intend to make on this machine, but I have to question it's suitability as a first lathe. Do you have, or are you willing to bring in sufficient power to run this machine? Do your plans include eventually acquiring a properly sized mill so that you can offer complete projects? A lot lathe work has some mill work on it somewhere, and to do business, you have to offer the complete package if you hope to get that kind of work.