Don't skimp on the bike. Let me ask you this: if you had to train for running ONLY on a treadmill, how much would you budget for that?
A bike is an investment and will last a LONG time if you get a decent one. So even if you spend $1000 for an entry level bike, that's only $200/year if you keep it for 5 years. How much will you pay to use a pool to train for the swim? Once you buy the bike, riding it is free.
If you do buy a used bike, you need to get fitted for it. A shop will probably charge you $100-$200 for a fitting, so unless you know an experienced fitter who will do it for free, factor that into the cost of a "used" bike.
Finally, if/when you are fitted, it's likely that you might need a different saddle, stem, or other part swapped out. Many shops will either swap out equal parts for free, or simply charge you the difference. If you buy used, you pay full price if/when the bars are too wide or narrow, the stem is the wrong size, or the saddle is a bad fit.