I know that in 1984 the Party wants power just for power's sake—but what kind of power does Winston strive for, and how does he accomplish it?

The novel opens with Winston's opposition to the Party and the government of Oceania. He writes "down with Big Brother" over and over in his new diary, and hopes that there truly is a "Brotherhood" in secret opposition to the regime. He dreams of having a real conversation with O'Brien, who he believes is a kindred spirit. What Winston wants, however, is not power over others but power over his own life in the form individual autonomy and objective truth. He wishes the current government to end so that he can live something approximating what was an ordinary, mundane life during his childhood or the years before he was born. This includes not being under constant surveillance, being able to freely think his own thoughts without it being a thoughtcrime, having a genuine, intimate relationship with another person in privacy, and living in a world that at least tries to record history in an accurate way, rather than rewriting it at will to accord with the current political agenda. So, personal freedom, privacy, relationship, truth-telling: these are the modest forms of power Winston strives to achieve. 

For someone as downtrodden as he is, living in such a closely regimented police state, he works vigorously at and achieves, for a short time, a surprising number of his goals. He asserts personal autonomy through his diary, he visits Mr. Charrington's shop, and maintains his own memories, such as that airplanes were not invented by the Party. He achieves a physically and emotionally intimate love relationship with Julia. He tries to attain a measure of personal privacy in the wooded areas outside of the city and in the room above Mr. Charrington's shop--he and Julia certainly work hard and take risks to achieve this impossible goal. 

He also takes steps toward joining the Brotherhood, primarily by visiting O'Brien's apartment with Julia. He believes O'Brien is part of the movement to overthrow the state and he willing joins in. He doesn't know O'Brien is deceiving him. 

Winston shows a large degree of autonomy and agency in trying to achieve his political agenda before his arrest. After his arrest, he resists capitulating to the lie that two plus two equals five and is determined not to betray Julia, though in both cases, the state breaks him.