I've given an opinion on this subject here recently. If you want to be a prosperous hobby farmer you can buy a small Kubota tractor and accessories to suit; put enough zeroes on the cheque and you can get a pretty good outcome. I think your property is too small for a 'real' tractor (anything with a 'Category 2' 3-point linkage) but there are several small ones of various degrees of merit available pretty cheaply second- (or more likely ninth-) hand. You do not have to use a slasher to mow your grass - you can get various kinds of 3PL mowers, including cylinder type. A slasher will not give you lawn, it will give you pasture. It's pretty good for flinging horse turds all around and making them invisible though, and it is less affected by the odd two-kilogram rock than a mower is.
Many people with small pasture areas find they need to do things that call for cultivating, or at least harrowing, their grass fairly regularly. They also need to repair erosion, bury pipes, rip tree-planting lines, etc. The enthusiasts end up with 3PL attachments for driving wooden fence-posts, drilling holes in the ground, grading farm tracks, and all kinds of fun stuff. You can test the waters on your interest in this kind of thing by going to a few clearing sales and talking to farmers about the how and why for each piece of kit.
The cheapest solution to your problem is to get a cheap grey Fergie with a petrol engine (for heaven's sake do not buy a grey or early red Fergie diesel: they had a diesel head on the petrol engine, and it is an evil contrivance. You can get old and irritable just cold-starting the thing.) By the time they put the Perkins 3-cylinder diesels in them (mid-1950s)they became nice tractors, and are priced accordingly. Once you have the tractor issue under control, continue to hang around the clearing sales each weekend, learning and gradually acquiring accessories. I used to enjoy clearing sales, though I actually bought most of my kit from junk-dealers and private sales.
