A couple of extra thoughts to those above John. Aside from financial considerations, is there any reason you don't take at least a few lessons? A good teacher should be able to help with all of these things, much better than us lot, due to the direct observation they can make of how you are doing things.
Re the guitar specifically, well again a tutor would be in a position to advise, and may well save you unnecessary expenditure on different guitars, as it is possible its not so much the size of the guitar as its position in the budget range that makes it hard to play. Going to a guitar shop and trying out a few decent ones briefly would also be one way to check that out. As you are in Leicester there are a couple of guitar specialists within an hour or so of you and they would be able to make a number of potentially useful suggestions. I really would advise against just ordering something online and hoping its what you need.
Re nerves, to amplify the points above, the crucial things are i. playing things that are really easy for you, ii. doing it often and regularly. Its very like an inoculation.
If one is playing pieces like Lagrima, Adelita which are around grade 4-5, perform pieces about half that, e.g. grade 2, but having learnt them very thoroughly. Doing so helps make a positive start upon which to build, and then over time, as confidence and experience improve, gradually and sustainably increase the technical level of the pieces chosen. Also, if you have time to play two pieces, normally make the first one something really really simple, and then the second one can be more ambitious and have more chance of success, as you have had time to settle down, get used to the situation, the sound of the room, the fact that people are looking at you, etc etc.
It goes without saying that one can only have confidence in performing a piece that one knows inside out and can reliably perform easily at home. But how one learns in the first place, and then over time, practises a piece, also comes into play (pun intended). Simply playing a piece from end to end time and again is not a good way to practice! Isolate the tricky bits and do them repeatedly and analytically, maybe not bothering all the time with the easy bits. My most powerful technique is to rehearse the sections in reverse order - e.g. the last 4 bars, then the previous 4 etc, always ending on the first beat of the succeeding section, so the joins are smooth.
Also, just come to terms with the fact that pretty much everybody suffers from nerves (even youngsters, but they rarely show it), its normal and natural, and you are not the only one afflicted with this dis-ease.
If you really can only perform say once a year, I would simply stick with playing maybe a group of really really easy pieces, maybe by the same composer.
If you decide to think about lessons, get in touch with Yvonne Bloor, who should be able to help, or suggest alternatives.
Simon Ambridge Series 40 (2005)
Trevor Semple Series 88 (1992)
Louis Panormo (1838)
Alexander Batov Baroque Guitar (2013)