I don't think that there's a single answer here for you, not least because "communists or socialists" is a huge heterogeneous group of people and ideas. I can give some recommendations, but only from my own perspective, not as a representative of socialism or anything.
First of all, if the responsibilities of the position you're voting for could reasonably be fulfilled by anyone in the group, you can probably just draw lots. The fancy technical term for this is sortition, and combined with short terms (where the definition of "short" depends on what your organization is doing) it's a good way to prevent abuses of power.
If you're either electing for a position that needs particular skills or you don't think you can sell sortition to your group, I like approval voting. You can vote for multiple people, and you just vote "yes" on anyone you think would be a good fit. Whoever gets the most approval wins. It's a good, simple way to ensure that most people are okay with the outcome, even if the winner wouldn't have necessarily been everyone's (or anyone's) first choice.
Finally, the things you're asking for make it sound like you need some advice on how to actually run the election. I will always recommend anonymous paper ballots: most electronic schemes are harder to secure and easier to de-anonymize. You can make them work, especially for small groups, but it takes some thought. Also, paper is easy to set up, you just need a printer and a locked box to keep them in.
You can count the results in a group to ensure that's done fairly, and throw out any ballots marked with anything other than votes if you're concerned that someone in the org is trying to influence people illegitimately. Run the election for long enough that everybody could reasonably have a chance to show up and drop in a ballot. You can lock the ballot box with two (or more, depending on level of paranoia) keys held by different people if you're concerned that just one single keyholder might be corrupt or corruptable. Proxy voting can help if there's someone in the organization who you know won't be able to make it in person, and that should be easy to coordinate with a small group if you need to.