Do what is most enjoyable and relevant to your own goals at that moment. If you just want to practice speaking, then pick a topic that you really want to discuss. If there’s a grammatical issue that needs clarifying, then ask… You can do both in any session, according to your needs and interest. I recommend starting with a 30 minute session. If you find this easy, you can always increase to longer sessions as you feel comfortable.
In my own Skype sessions, I generally prepare a topic that I want to talk about. This way, I make sure I know the key vocabulary. Like you, I am not looking for a tutor to teach me new words, but rather I need to practice conversing, using the words that I already know. During our session, my teacher asks me questions (as she would do in a normal conversation) and writes corrections on the side of the screen which I can then print and review later. (I have never done this, but if you figure out how to record these sessions, you could review them later.)
Sometimes I come to the session with questions. Sometimes it’s about a grammar point or about word usage – two words are similarly translated in English but are used differently in my target language. Even though I prepare for a lesson, I generally learn a few new expressions in the course of a Skype conversation. I always receive corrections.
The topics vary considerably and change over time as my knowledge increases and thus conversational options expand. As an upper beginner, I originally talked about things that were of immediate relevance to my life, often using vocabulary that I learned from a LingQ lesson but then applied to myself: e.g., the history of my city, how I spent the weekend, a typical morning, etc. As my vocabulary increased, I have been able to talk about TED talks I’ve watched as well as items in the news.
By contrast, some teachers have lessons they give students (especially at the beginner level) – e.g., something to read or a video to watch. The teacher then can then tailor the session around that content. This could work, provided the material is well-matched to what you find interesting and your competence level which is not so easy to achieve. I would guess that you’d have to have a few sessions with the same teacher in order for the latter to know what you like and what level material you can comfortably handle. For me, something that is too difficult is de-motivating. By contrast, something that seems easy may be very motivating because then you would feel very confident about talking about it and can expand on the topic, just as you would in a normal conversation. (That reminds me of…)
I recommend being flexible and that you try different strategies to see what works best for you. If you feel energized and motivated after a session, that’s a good sign! If you feel discouraged and overwhelmed, then it’s time for some tweaking of your expectations/approach.
Keep in mind that for most adults, speaking is the hardest skill in language learning and often lags behind their skills in reading, writing and listening. Good luck!