I am assuming that you are referring to documents such as your personal statement which you will be uploading to LSAC.
Times would be the safer route to ensure that it is seen in the manner that you have sent it out. While Helvetica is considered a browser safe font as web browsers from multiple platforms support the font, it has an odd history in the world of MS Office, especially on Windows machines. Given that you will likely upload your statement in a .doc or .docx format, someone else (perhaps several people) will be looking at this on computers which you do not control. As such it will be left up to their computers how to interpret this document. If the tool that they are using does not 'recognize' Helvetica, then it will choose an alternate (likely Arial) to display your document to them. If you are OK with Arial or some other font being substituted on the fly, then you have nothing to worry about. If on the other-hand you would prefer that those reviewing your statement see it as closely as possible to the manner in which you sent it, then you may wish to send it in a font that is likely to be present on any possible machine and software that might be looking at your statement.
As for size, 12pt seems to be advisable, several people have commented that 11pt can be used if you really need the extra space, but I would not push it further, and I would make a strong effort to stay at 12.