Ben Fine is a semi-Stalinist, but his "Marx's Capital" (more recent editions co-written with Alfredo Saad-Filho, who is not a Stalinist) is probably the best for someone who has no background in standard bourgeois economics.
For someone who has some background in standard bourgeois economics, I think the best book is still "Economics, an anti-text", from the 1970s, by Green and Nore.
Second-hand copies available cheap from Amazon. I think Sue Himmelweit's, Simon Mohun's, and Ben Fine's pieces are particularly good.
David Harvey's "Brief History of Neoliberalism" https://www.amazon.co.uk/Brief-History-Neoliberalism-David-Harvey/dp/0199283273 is informative and accessible, though I think theoretically very weak (see http://www.workersliberty.org/files/170801neoliberalism.pdf). It may be good for someone with no background in economics at all.
"Capital" is not as hard as it's made out to be. Try starting out with chapter 10 on the Working Day, and see the resources at http://www.workersliberty.org/study#capital
Otto Rühle's abridgement http://www.workersliberty.org/ruhle may be useful for people who find the sheer length of "Capital" off-putting.
Harvey's "Companion to Marx's Capital" https://www.amazon.co.uk/Companion-Marxs-Capital-David-Harvey/dp/1844673596 is ok-ish (except on chapter 15: see my stuff about it at https://capitalvolume2.wordpress.com/), but it's a companion to Capital, not a freestanding text.
Luxemburg's "What is economics?" is, I think, very good - http://www.workersliberty.org/story/2017-09-07/rosa-luxemburgs-what-economics. But it is methodological, so suitable only as a first short read before going on to more substantial stuff.
My "Crisis and Sequels" http://www.brill.com/products/book/crisis-and-sequels should be valuable for people with little background wanting to understand the economics of today. Brill will publish it at a huge price, but university students should be able to get it through their university libraries.
An easy-to-read and informative book about the 2008 crisis, by a Marxist: David McNally's "Global Slump".
Richard Wolff https://www.amazon.co.uk/Richard-D.-Wolff/e/B001H6PV5A is nominally Marxist, and prolific. However, Wolff is theoretically an Althusserian and post-modernist, politically a Green. His book on the USSR is terrible, pompous, pretentious, waffly (see review, below), which does not recommend his other writings.
Ha-Joon Chang's "23 Things They Don't Tell You About Capitalism" https://www.amazon.co.uk/Things-They-Dont-About-Capitalism/dp/0141047976 is well-written and debunks some right-wing myths, but is not really a place to start on economic theory. It is avowedly pro-capitalist.
Paul Krugman's books https://www.amazon.co.uk/Paul-Krugman/e/B000APS32M are useful if you want a readable soft-neoliberal response to hard neoliberalism.
Ernest Mandel's writings are widely available but not good. His "Introduction to Marxist Economic Theory" is terrible, especially on fundamental things like the labour theory of value.
His "Marxist Economic Theory" is extremely long, and very shoddy in some crucial sections.
His "Late Capitalism" is a serious effort, but wrong on almost everything. See http://www.workersliberty.org/node/24447
I think his "Formation of the Economic Thought of Karl Marx" is quite good, but it's a book to read when you've already read a lot of Marx.
If you want to know a bit about radical left-wing variants of Keynesian theory (almost all serious economists are some sort of "Keynesian", even the hard neoliberals), then start with Steve Keen: