I know your question was answered by another user, but I wanted to add some additional information to help both your understanding of the grammar as well as anyone else that comes across this point in the thread.
According to you this would be the context:
And you presented three different answers
～てみる indeed means to try to do (something) @NicoleIsEnough mentioned that this grammar gives the nuance of trying for the first time. Although it can have this meaning, there’s a deeper meaning with ～てみる that often doesn’t get highlighted despite this grammar being well used. According to this website (see points 2-4), this grammar means to try to do something even though you don’t know how it will turn out or whether it’s the correct thing to do. Essentially it softens the action it’s attached to by making it sound reserved or the lesser extent.
So in essence, 考えてみるね almost sounds like a soft “no” because I think it almost sounds like not much effort will be put into the thinking.
The second sentence sounds like this wasn’t the first time this question was asked because of もう少し. The addition of もう少し implies that the action has already started and the person saying the statement will take additional time. This was referenced in this yahoo questions posting. The person asking wanted to know what was longer 少し and もう少し. Although I understand that it’s obliquely related based on the examples used on that site, but I think that meaning is applicable here too. In other words, もう少し考えてみる means “(I’ve said I’ll think about it, but) I’ll try to think about it a bit more”. I can’t tell you whether this is a stronger commitment than the first sentence, but it does contain the meaning of thinking about something a little longer. So if the original question was asked for the first time, the second response doesn’t sound really natural because it would probably imply that you had considered the listener’s question before they had even asked it.
Lastly, ～ておく was also correctly identified by NicoleRauch as to prepare something in advance but there are additional uses for this grammar as well. I’ve written about ておく before so I’m going to quote the part of the post that’s relevant.
According to this website , ～ておく has shades of meaning besides just doing something in preparation for something else. In fact it lists 4 different uses:
- Preparations in advance (i.e., for something happening in the future, carry out relevant preparatory actions in advance)
- Dealing with things temporarily (i.e., as a current measure, tentatively act)
- Preserving a state (i.e., a continued state which is not tampered with and left alone)
- Retained result (i.e., to leave behind the results of actions done previously)
Since there’s no equivalent structure in English to express ～ておく, it’s often oversimplified and when used in different contexts (like in the case of the three other uses) it difficult to why it was used if one only knows about the first meaning. I agree with Nicole that the response that uses this grammar sounds more committal than the other two (like “I’ll think on it”) because the speaker intends on following through with the action, but that’s just my own personal opinion.
Hopefully that adds additional insight for you.