Some good advice here but I didn't see anyone mention if you buy an older tractor to make sure it has a two stage clutch, a necessity when bush hogging, and a 2 speed rear end. Some of the older American made and foreign made tractors do not have these two features. Very important.
If you have a pretty good mechanical ability, an older tractor will save you money. You might find a good used one that really has no problems, but the little quirks will be there, small adjustments or repairs will be costly if you can't do them yourself. If you know you will have to pay to keep things going, a newer machine might be the way to go.
Every piece of equipment is designed for its own use intent. A tractor is designed for field work, a lawn mower is designed for just that also. Buy both, you will find in the long run you will be happier unless your yard is wide open with basically no trees and landscape. I have a neighbor that cuts his grass with a tractor/finish mower and is constantly saying he wants a lawn mower.
As far as owning a trailer, I am a self sufficient person, do not like to have to wait until someone else has time to do it. I say yes, you need a trailer. You probably aren't going to buy a really large tractor, so therefore you won't need a really heavy duty trailer, atleast not one rated for heavy equipment.
Keep in mind, the bigger the tractor, the more it cost for maintenance and upkeep, operating costs. Figure out your needs and buy big enough to get the job done but don't over do it. Also, bigger tractors require bigger storage sheds.
Storage sheds. Why does every farmer keep his equipment in a shop or under a shelter? He knows they aren't water proof, they allow water to seep in by the shifter and levers. A properly stored tractor looks better, lasts longer, has less problems and maintenance. I hate to see any tractor sitting out in the weather. Plan on storage costs too, well worth the cost to protect your investment. Mother nature is not kind to tractors left outside.
Not knowing how free money is with you, but the Yanmar line of tractors is a cheaper way to get a tractor for less money. If you do look at this route, stay away from the ones that have been refurbished and have hardly no hours on the hr meter. Some were rebuilt in Vietnam by shady dealers and are nothing but trouble. But some of the Yanmars are great lil low cost tractors. I have a 2200 YM, it is a great tilling or cultivating tractor but does NOT have a 2 stage clutch, not a bush hogging tractor by any means.
When it comes to plows and implements, watch Craigslist, lots of deals out there sometimes. Used tillers are usually expensive, the cost of tine replacement is usually pretty high.