Getting into 250 racing
So, you want to maybe find a Ninja 250 and go racing on it. Open your wallet. Racing is expensive. That said, the Ninja 250 is one of the least expensive ways to do this. You'll be looking at a couple to several thousand dollars by the time you get through the first season, but that favorably compares to 600 Supersport racing, where you can't really get started for less than $10,000.
The first thing to do is, of course, find out if there's a race series near where you live. The Ninja 250 is slow by most race standards, so being able to race exclusively with them is usually less intimidating than running in a mixed class. You should already have done some track days, so you will know where your local track is. Use their resources (phone, website) to find out which organizations hold races there. You can also follow the links under Finding a track school.
Then you'll need a bike. A dedicated track bike. You don't want to (and usually can't) race your daily rider. Up-front costs will include, among lots of other little things, new tires, a new rear shock, new fork springs, new fork oil, and whatever repairs will be necessary to bring it up to good, rideable condition. It doesn't have to be a pretty bike, but it's got to be mechanically sound. Plan to replace the coolant with water (and change it back when winter comes). You may want to get some secondhand fairings. You will crash.
Factor in race organization fees, entry fees for races, and money for practice sessions, be it with your club or as track days. Other expenses depend on how much stuff you already have. Even the most basic leather suit is going to be about $500, and you may need extra gloves, boots and helmet(s). You will crash.
You'll need at least a swingarm stand, since your bike will no longer have any stands on it. A front stand wouldn't hurt. Also plan on going through some parts. The front brake reservoir is a likely casualty in a right-turn crash, as are the footpeg side plates. Clutch and brake levers, obviously, and new footpegs, rear brake, and shift levers would also be worth having. Anything you can see easily getting ground off, snapped off, or snagged on something as the bike slides on its side down the track is a good candidate. See Spares to bring to a track day.
You'll need a minimal set of tools to take to the track. Duct tape makes for acceptable temporary fairing repairs.
Plan to strip everything off the bike that doesn't hold it up, make it go faster, or make it slow down very quickly (see here). This should include lights, fenders, unnecessary bodywork, gauges, stands, locks, and more. For most people this will also include an aftermarket exhaust, as the stock cans are heavy. Check the regulations before you spend that kind of money or make any major bike changes. To give you an idea, see IanJ's racebike log.
If you know your way around a Ninja 250 pretty well, it's probably two solid weekends of work to get the bike stripped and get everything race prepped, with safety wire in all the right places. Again, check the regs for the series you're going to be riding.
Being at the race track is a lot more pleasant with a pop-up shelter, some chairs, a cooler with food and beverages, and other creature comforts. Those are things you may already own, of course. You'll want to have a large (5 lb+) fire extinguisher close by. You'll need some variety of fuel can, as a lot of tracks don't have a gas station and are BYO. If you don't have a truck or trailer, you'll need to get one, or rent one every time. And so on.
Have fun. Racing's a blast.