When purchasing gear, don't be afraid to do a little research by visiting the various manufacturer's websites. Granted they will all tell you that their gear is the best but look at the various features and benefits that the equipment has to offer.
Make a list of the types of diving that you currently engage in and the types of diving that you might see yourself doing in the future.
Does the piece that you are looking at fulfill those needs.
Realize that no manufacturer can afford to make a bad regulator but you may find that some of the "bells and whistles" either more or less suitable for your needs.
Try to keep at least the regulator, occy and computer to one manufacturer as this makes the serviceability aspect so much easier. Having to take your main regulator to one dive store for its annual and your occy and computer to another can get tedious and expensive.

If your budget allows, see if there are package prices. Packages usually consist of a regulator, occy, BCD and gauges/computer and are generally cheaper in the long run than buying piece by piece.

At all costs, avoid buying used as any and all manufacturer warranties are for original owner only and are null and void when purchased second hand.

If buying online or in a physical "brick and mortar" dive store check the manufacturers' websites to make sure that they are authorized to sell and service that gear. If they aren't and you purchase from them then it is considered second hand.

Check the serviceabilty of the equipment. If you have a problem out of the country will you have a problem getting your equipment adjusted or fixed?

If you had to buy from scratch my advice on order of importance would be as follows:
1. Mask (give your girlfriend a kiss on getting the prescription as it is so much better seeing while diving than not), fins (boots if needed) and snorkel (you will be prepared for snorkeling and can rent if you dive)

2. Regulator (complete with occy and computer gauges) This portion is your life support and at this point you are prepared for scuba (both at home and abroad) and can still rent BCD and other gear as needed.

3. If bought separately then a BCD (tanks and other gear a can still be rented)

4. An equipment bag.

5. Dive tool i.e. knife or cutting tool

6. Exposure suit (suitable for the environment that you will be diving in the most i.e.cold or warm water) If most of your diving is cold water then get the cold water suit before getting a warm water suit.

7. Scuba cylinder(s) If the bulk of the diving you do is local.

8. Weights This is last on the list because until your exposure suit is broken in and you have dove with all of the above for awhile, the weight needed will fluctuate. Purchase weights if, again, the bulk of your diving is local.

I don't think I missed anything but if you have questions on fitting gear check out the gear guides and videos on how to fit gear at the links below.