How much $ needed to get strated in triathlons?

If you own running shoes, a swim suit and a bike - nothing.

If you are thinking about doing a tri, you should start with what you have. If you like it then you can spend some money on upgrades.

What is a running shoe? It is a shoe made specifically for running - not a pair of cool looking athletic shoes. It should be a pair that offers the support and cushion uniquely required for you. It should not have more than 400 miles of combined running and walking miles on it. If you run in worn out shoes or the wrong kind of shoes or shoes that don't meet your needs - you will get injured. Medical bills cost more than shoes. Buy some. Ideally you should go to a running specialty store to get the right shoe for you. It will cost more (~$95)than at a department or sporting goods store (~60). But you will save your self injuries and set backs in training. You will be a stronger , faster runner. You can get your next pair at a discount store. Just buy the same shoes. trust me the extra $30+ is a good return on your money.

Can you ride your 1995 Murray mountain bike? Yes! But if that is all you have, try to borrow a bike for a few training rides and the race. A friend of my wife's tried to ride a full suspension Huffy on a 30 mile tour. The bike had to weigh 50 pounds. It was brand new but every component was garbage. She would have done as well to run. She was unable to finish the ride. My wife used a 5 year old Giant Boulder (pre suspension) weighing 35lbs with high quality components. I had also swapped the over sized knobby mtn tires for road tires bought at Target for $10 each. It was an easy ride for her. My friend Vicky used this same bike for her first Triathlon last year. She couldn't believe how much nicer it was than the department store mountain bike she was trining on. A bike like that used $50. An entry level bike that can be used for multiple purposes (niot just Tris) is the Schwinn Super Sport at about $400.
If you want a road bike Target sells mass consumer level Schwinns. I used a Schwinn Prelude ($178) last year and loved it. A friend of mine borrowed it for a Tri as well. They are available at Target and Amazon for a little over $200 now. It was a little big for me and I am getting serious so I ....well, I'll get to that in a later post.

Put simply train on what you have. Borrow a bike if need be for the event.
You probably will wear the same shoes on the bike and run (until you upgrade to clipless pedals)
Oh, and if you don't have toe clips head to Target and get some >$10 - it is a HUGE difference.

What kind of swim suit do I need? What evere you have. woman's one oiece or men's trunks.
I bought a triathlon specific swimsuit srom Club Swim for $10 - they are like biking shorts but they don't come down as far and have less padding. The are swim suit material. I train in really big baggie swim trunks - please fellas - leave the speedo at home when you go to the city pool.