Welcome to the forums jenniferry.
Your LG drive is a 20x burner, so it is not too old, and should be fine for your purposes. You might want to check at the LG site to see if there is an updated firmware for the drive. To see which firmware you have now, you can use a free tool like Nero InfoTool.
-R or +R doesn't matter as much as getting good quality media. Sony normally is decent, but we recommend Verbatim 16x most of the time around here. Another safe choice is Taiyo Yuden 8x +R, which can be found at online shops like rima.com or supermediastore.com. Those are for regular, single layer dvds.
It is possible to bitset +R disks so that they look like commercially made dvd rom disks, and so, increase the compatibility with stand alone players. I believe Nero can do this, and I know that ImgBurn can do this with LG drives. ImgBurn is a free burning program. If you are interested, let us know and we can outline the procedure.
If you are using double layer dvds, the only ones reliable enough for us to recommend are Verbatim. They should be bitset automatically by your burner.
LG drives do have a reputation for being picky about media, so you should use the best available in it.
If you are burning 16x single layer disks, you should slow down the burn speed to 8x or 12x for best results...no slower. If you still have more of the Sony disks, I'd try 8x with them.
Now, on to your dvds going to the UK. The US uses NTSC standards for dvds, which regulates the resolution, frame rate, and types of audio used in the dvd-video. The UK uses PAL format. Fortunately, most PAL equipment can play NTSC video without issues. If you want to be certain, you'd have to reencode the original footage in Ulead and have it output in PAL standards.