Ripping my movie collection

In preparation for my move to KSA, I want to copy my DVD movie collection to digital. Does anybody have tips on the best way to do it? Best software? Unforeseen problems during playback? I have both Mac and PC: same software?
And should I bring a HDMI cable, or just buy one in country?

I believe one way is just to purchase an external DVD burner. 
I used to have one, but don't have any specs for you, sorry.

It was a fairly straight-forward process.  The software was included.

I'd imagine one type would be for WIN and another for Mac.

Buy and HDMI in country.  They're isn't much of a difference in price.

Assuming your collection is legal, there are no copyright issues in making a single copy for your own use.
There are many ways of doing this, but they all require time and effort.
When I decided on the move to Indonesia, I had two laptops ripping my DVD collection every free moment I had.
Loads of software around to do it, so no worries there, but you have to decide the output quality against available storage space.
At the time, I ripped most to WMV at quite a low quality because I simply didn't have the hard drive space to do much more, but high capacity drives are easily available now, so I would suggest you save at a higher quality.

If you're really pushed for time, and have loads of drive space available, you can simply copy the DVD's files directly to a hard drive, but most films are a little over 4gb each, so drive space runs out a lot faster than if you save in AVI or MKV, usually at 1 gb or less, but still maintaining good quality.

Direct copying of DVDs, without processing to another format, would allow about 238 films onto a 1TB hard drive.
Remember to set up a folder for each DVD, then just drag and drop the files.
With processing to another format (Less a gigabyte each), you'll get a thousand or more on the same drive.

Any advice on formats? AVI, MP4, MKV?

AVI will produce good results and is playable on almost everything.
MKV is more up to date, and better for larger screens, but some portable devices still won't play them.
The same goes for converter software - all do AVI, but less will encode as MKV.

If you intend to use smaller TVs, computers, portable devices, and so on, it has to be AVI.
If you want to play on large screens, go with MKV.