Let's say your budget is $1500. I have taken the liberty to show you how you can begin training using data for less than this budget.
Run data collection
Garmin is the major player, dominating the market, and even as they have introduced nicer models, they have also introduced cheaper models with effective features, such as downloadable data, ANT+, and done it with much more aesthetically pleasing watches, unlike their original and bulky Forerunner 205/305/310XT models.
I recommend Garmin's Forerunner 210 model. It does it all, small on the wrist, acts like a normal watch too, at $299 on Amazon. There's a 110 model for cheaper, but the 210 gives you all the important data of pace, heart-rate and cadence on the run, (via foot-pod). The 110 is not as good, as the 210 comes with everything you need to download the data as well, is the better investment.
I recommend splitting up the computer units you'll use for the bike and run. Come race-day, this is faster and easier. Also, it helps to save battery life if one unit isn't doing all the work. When you have a dead battery, you have no data.
For the bike and power data, a single wireless unit with ANT+ capability, like the Garmin Edge 500 is a great unit, available at Amazon for $249. You can purchase this model without a HR monitor, because the one with the 210 is compatible with this one as well, so two for the price of one!
The easiest power meter on the market is the Powertap, and it is priced extremely cheap at $660, with ANT+, on an excellent training wheel at Competitive Cyclist. You won't need the computer head, because you've got the Edge already.
Total cost for this combination: $1208, ($292 below budget!)
If you want a race wheel, you can use the savings from the budget to buy a nice front wheel, and then go to Wheelbuilder and get a disc cover, (Aerojacket), for your training wheel. It will make it suddenly a great racing wheel, and in some studies, even better!
Run data collection and Power data collection in one unit
Though I mentioned above that I'm not a fan of one unit for both, some people are. The best unit for this is either the 910XT, ($449 at Amazon), or the 310XT, ($349 at Amazon), both listed with the heart rate monitor.
Here's the 910XT and the 310XT...
You will want to buy the foot-pod, as cadence data can tell you a lot of information about how your running is. It is $88.94 at Amazon, and is compatible with both the 910XT and the 310XT.
Again, the Powertap from Competitive Cyclist at $660, with no computer head, is still the best deal.
Total cost for this combination:
$1197.94 for 910XT, with foot-pod and Powertap
$1097.94 for 310XT, with foot-pod and Powertap
This last single-unit combination is not much lower in cost than the 2 unit combination, so consider the advice of separating the two. Also, you can use the savings to get a disc cover mentioned in combination #1.
And last but not least, is the software to analyze. This is the best part, TrainingPeaks is FREE! If you want some bells and whistles, you can pay for a premium account, but if you have a coach who uses it, you likely get the premium account included in their services.
You can truly see how a $1500 budget is more than enough, and as little as an $1100 budget will get you using data and taking your training and performances to new levels! No more excuses, time to do it right!