Wow, what an open question. To help I'd make the following recommendations:
1) If you're not sure if this is for you, buy a used machine. Lathes (well looked after) tend to lose value from new to second hand and then further depreciation is very slow so if you buy a used good condition machine and look after it the trial won't cost you too much even if you decide it is not for you in the end.
2) It's not just the lathe. I don't know what other kit you have but you will also need a grinder to keep your tools sharp (basic 6" machine with a white Al Oxide wheel is the minimum really, ideally a 40mm wide wheel but not essential). Also you need a set of tools. Prob 5 or 6 to get you going - roughing gouge, 19mm skew, 3/8 bowl gouge, spindle gouge, parting tool and round nose scraper would make a good start. Can be bought used on eBay by package deals from the likes of Axminster almost same price.
3) Type of turning your looking to do. Without stating the obvious, this will really dictate the lathe for you. If you are looking to throw a rough 2' diameter log onto a £160 machine and expect it to perform then sorry but think again. I note you are a tree surgeon and so you will probably be rough turning plenty of wet (therefore heavy / off balance) pieces compared to a 'normal' hobby turner who may purchase dried and prepared blanks commercially. Therefore a degree of heft is of significant advantage, if not inherent in the the machine, needed to be added as part of mounting arrangements.
Having said above, 'type of turning' breaks into two main areas - bowls / vase forms etc and stick / spindle work. Both have lathes more suited than others with many jacks of all trades also avaialble. More info needed really to recommend a specific type.
So, have a think / browse of the type of stuff you would like to do and I'm sure I / we can help some more.
Welcome aboard, I'm sure you'll enjoy your turning, almost all who try it do and stick with it. Feel free to ask anything here, we're a friendly bunch.
BRgds
Simon