I looked into it for L3301 and in short, you want at least 10k GVWR trailer... Trailer itself will weight ~2-3k. Tractor loader backhoe (or some other heavy rear attachment) and filled tires is around 5k. That's going to be around 8k of weight already. Then you might want to bring extra attachments for 1k or hold something in pallet forks etc. Also should consider what if you were to upgrade to heavier equipment. A 20%+ buffer is good, so 12-14k is a good 'sweet spot.'
You need at least 18 foot trailer... 16 will be too short and ideally you probably wans 20 foot+ (but they start to weight more). My tractor sits in a 24 long garage. There is only 3 feet extra space front and back... (24-6 = 18). Equipment trailers will have kinda misleading numbers... for example an 18 foot trailer is actually 16 foot of deck with 2 foot ramp/dovetail in the back. It can still work, but it's smaller than you think..
End of the day, it costs 5-6k+ for a properly sized equipment trailer. New OR used (not much discount).
It's not worth it unless you need to transport a tractor often or to make money with it. Or have other reasons for the trailer...like people mentioned they have a dump trailer for dumping etc and use that. Also storing the trailer and keeping up with it might be a problem for some. Handling such a large trailer and having the proper truck to tow it is something to consider...even though full size 3/4 trucks can tow 10-12k now a days, that requires weight distribution hitch, gooseneck, etc. Lots of dangerous situations you can get yourself into...
I think pretty much all dealers will pickup and return your equipment for a cost. Yea it's not cheap, but much cheaper than owning a trailer.
Last... I would just do the maintenance yourself. I changed all the filters and fluids on my L3301 last week and it wasn't hard. Second time will be even easier...as long as you have the proper tools, it's very consumer friendly to service...plus you save cost of dealer doing it, transport, and etc. That could add up to be $500+ that you could use instead for something else.