Feel free to read around Clare's poetry as your interest takes you, but it may help to focus on the following from the Oxford World's Classics edition:
From 'Poems written in Epping Forest and Northampton Asylum': 'The Gipsy Camp' (278); 'Child Harold' (279); 'Spring' (328); 'Sonnet' (345); 'Spring' (356); 'I Am' (361); 'Sonnet: I Am' (361-362); 'The Autumn Wind' (372-373); 'Clock a Clay' (391-392); 'Autumn' (405); 'Birds: Why are ye Silent?' (415-416); 'The Yellowhammer' (417); 'The Maple Tree' (423); 'Fragment' (427); 'John Clare' (427)
From the prose: '[Journey Out of Essex]' (432-437); '[Apology for the Poor]' (445-446); '[The Poor Man vs. the Rich Man]' (450-451)
And from the earlier poems, look especially at ‘The Lament of Swordy Well’ (147-153); ‘The Mores’ (167-169); 'To the Snipe' (205) and others from 'Bird Poems' (205-243; note the number of poems on birds' nests); the 'Animal Poems,' esp 'The Badger' (246) and the later poem 'The Mouse's Nest' (263); 'The Flitting' (250) and 'Autumn Birds' (267). Note the series of poems on 'Gipsies' and their camps throughout Clare's oeuvre.
Raymond Williams’s The Country and the City is an essential contribution to the ecocritical canon, but for our purposes we'll be focusing on the introduction, "Country and City," and Chapter 13, "The Green Language" - though note as well the important chapter "Enclosures, Commons and Communities."
A 1980s film of Williams explaining the book has recently re-surfaced and is worth taking a look at:
https://www.mikesouthon.biz/portfolio/the-country-and-the-city01title1
Finally, I've attached a bibliography on Clare if you'd like to do further research on him.