Hi there,
Firstly, welcome to the forum. Secondly, FW 3.18 is fine.
So, I'll provide a few links that should benefit you:
This article includes a list of good games to grab for a kernel exploit:
http://wololo.net/2014/09/24/friendly-r ... -or-never/. TN-V, in case you're unaware runs like a psp on your vita, with the xmb and everything. So, you can use most if not all homebrew, emulators and your backups. Please note however there are issues with volume if you run PS1 games through this exploit.
To transfer your game you can read this article. Check the sections "Getting a exploit game (or any other content)on to your Vita via OpenCMA PS3 trick" and "Activating and Linking a PS Vita (PS3 Required)" as they are both relevant to you:
http://wololo.net/2013/04/17/lower-ps-v ... r-dummies/
Here you can find the exploit files you'll need (obviously matching the game you get):
viewtopic.php?f=56&t=39739
Here is the download page for Open CMA. As ss4gogeta mentioned, you will need to run in airplane mode:
http://wololo.net/downloads/index.php/download/1252
In case you are unaware, Open CMA allows you to transfer files while using lower firmware so it's a necessity.
If you'd like to flawlessly play PS1 games on your console then you can read this article:
http://wololo.net/2014/09/14/how-to-usi ... 1-exploit/. Please note that you will need to convert any of the games you wish to play through this exploit to an EBOOT.
You can also transfer games through FTP which is my preferred method, but you need to use OCMA to get "Vitaftp" on your console which is something mentioned in the next article. This article can help you use OCMA to transfer files, as there are some silly security implimentations by Sony. Please note: DO NOT use Urbanix as this article mentions. I'm pretty sure it no longer works. Use one of the games from the previously linked article regarding 3.18.
Anyway, check this out too:
http://wololo.net/2012/10/05/tutorial-h ... n-urbanix/
If you need any more help feel free to ask.