Make sure you buy at least a semi-professional model as opposed to an ‘occasional-user’ cheap one, which would undboubtedly turn out to be false economy. Anything less than £200 (if new) will probably not last very long, and it might be difficult to fix or to find spare parts if anything goes wrong. NB: electric chainsaws are in the ‘very occasional – and light – user’ category.
Stihl and Husqvarna (‘Husky’) are generally considered the best models, but Echo, Makita and a few others are not bad either. You can generally get parts for these models and they will last a long time if looked after. You can’t get left-handed chainsaws, by the way, so if you’re left-handed, you’re going to find chainsawing a bit more difficult.
For a wood stove user or a smallholder you probably won’t need anything bigger than a 40-50cc model, weighing around 5kg, with a 330-380mm (13-15″) bar. Even for felling trees, you can cut into the tree from both sides, so you can fell a 760mm (30″) diameter tree with that. For very large trees, you’ll want to do special training, which will cover the size of chainsaw you’ll need.
Purchase from a recognised brand dealer – for example, search for ‘Stihl dealers in Lincolnshire’ (unless you live somewhere else, naturally). They’ll be recognised by Stihl and they’ll be dedicated to chainsaws (and sometimes mowers), so they know what they’re talking about and can help when it comes to faults etc. General agricultural merchants may not know so much about chainsaws. Of course when you’re discussing your chainsaw with them, you’ll have to understand what they’re talking about, which is why you’ll need to be at least a little mechanically minded.
This is even more important if you’re buying second-hand. You’ll have to understand the terminology, you’ll have to check it and you’ll have to know what you’re looking for. It’s not for novices, but basically, a) do you understand it? b) can you start it? c) and if you can, does it tick over nicely, or does it constantly stall? You can find second-hand saws on eBay, and recognised dealers often have them too.