Thinking about moving to St. Kitts/Nevis

I am from SKB.  Like everywhere, there is crime and you should always be mindful and aware of your surroundings. 
That said, SKB is one of the most beautiful islands in the Caribbean with very friendly people, and a few not so friendly, but that is everywhere. The island is growing by leaps and bounds so many of the creature comforts you have now, you would still be able to find them there.  Keeping in mind that you are relocating to a Caribbean island for the island life experience and some of those creature comforts you may have to give up. 
For $300K, you can get a pretty good home in the Frigate Bay area which is the Mid to Upper Class area.  A good resource for finding homes is someone I know personally, very personable and helpful, and that is Brian Kassab, B Kassab Real Estate he would be the tall lanky guy in the back with the unruly hair.  Brian is a native islander and has lived his entire life on the island.  He knows the island, the culture, the people, the market!!  Another good resource for anything island life for expats would be any of the Pereira's.  A family of young men who are also native islanders and has lived on the island their entire life.   They provide recreation and entertainment for tourist and locals alike and their beach bars and tour groups are among the most popular spots for tourist, locals, expats and students; Pereira Tours,Reggae Beach Bar and Greg Safari's Tour.  If you are in to a more sophisticated dining experience you can always find many restaurants around that can afford you that, like Carambola Beach Club, Marshalls Dining, or many others. 
If you are a golfer, SKB boast of one of the best greens in the Caribbean, Royal St. Kitts Golf Club.  You're into boating, there's always the St. Kitts Yacht Club. 
Nevis is just as beautiful an island, if not as fast paced as SKB. But it is just a simple ferry ride over, and you can take you vehicle on the ferry.  The crossing is only 2 miles. 
Fresh water has never been a problem on the island.  On St. Kitts we say that we have the best tasting water in the Caribbean.  Like the US, hot, dry summers and insufficient rain usually prompt the authorities to restrict water usage.  But some homes are built with cisterns in the event that water is cut.  This happens infrequently but can happen for things like maintenance on a dam and rarely lasts for more than a couple hours to a day.  But it is island life and if you don't have water, there is always the ocean to bathe!!  That is a joke, in other words, it's not that serious.  Drinking water is always plentiful and bottled water available.  You can also install filters to your pipes for "safer" drinking water.  Power outages, fluctuations and surges do occurs and chances are you would experience it.  However, although it may occur more often that you are used to, maybe 3 or 4 a year, they are usually just a couple hours of inconvenience, rarely lasting over 24 hours.  This can happen due to severe storms (hurricanes) and the authorities disconnect the power to protect residents and the equipment. There are scheduled power outages for maintenance which are usually communicated.  Again, many  homes have generators to supply them with electricity if there is a power outage.  Gas stoves are used in most homes so a loss of electricity would not prevent you from being able to eat.  Your showers may not be steaming hot but who wants a hot shower in the Caribbean? The pipes leading to the homes are usually warmed by the sun, providing a comfortable temperature to shower.  If you can't look at cable, I'm pretty sure there is a beach bar open running on generator to provide it's patrons with entertainment (family friendly), food, and just good camaraderie. 
Most of the Doctors on the island are locals who were educated and trained in the US.  However, if you do not trust that the medical facilities are up to your standard, you can always pay a monthly premium to be a member of MASA Assist which can have you in the US for your medical needs.  But unless you have a major medical, there is nothing like the good Caribbean sun and sea with a couple local remedies you can pick up at the bar, to cure your ailments. 
How much money you need depends on what type of lifestyle you want to maintain.  The conversion rate is about $EC2.70 to a US$1.00.  Most places accept and quote prices in US$.  You may think that the cost of a gallon of milk at EC$20 is outrageous but when you factor in the conversion rate, import duties and the likes, it is not that much more expensive than buying a gallon of Pet Milk from the supermarkets in the US.  However, if you want to go Organic with food and get what is supplied on the island as opposed to what is imported from the US, then you would find that Organic is definitely cheaper on the islands.  Or you can always do like the locals and shop in the US and have the goods shipped by barrel.  Then you'd have to deal with the customs, the duty and all the shipping documents.  May not be worth your time but you'd get a better understanding for why something that cost US$5.00 in America cannot cost US$5.00 or even EC$15.00 on the islands.
If you want to move to any island, you have to understand that you are moving to an island.  You cannot go to an island and expect things to be the same.  You are moving to an island for what you assume is Paradise.  Well, Paradise is what you make it.  The islands provides the natural resources that they have available. You decided how  you want to use those resources.  Research the islands, know what you can and cannot compromise on.  Know what is important to you and what you want to accomplish from moving to an island.  Know and understand the laws of the land.  Respect the culture and the people.  Understand that Island Time is real!!!  The majority of people are not rushed and if an hour's lunch goes longer than an hour, then you're on island time.  Use the sun to tell the time and not your watch.  Stop and ask a local for directions (where you have to turn at the flamboyant tree by Ms. Babs house, the pink one...)  and not a GPS, you will get lost but you would have met some very colorful villagers who would only be too happy to help you out and chat a bit, but you may end up coming home with a bag full of mangoes, avocados, local fruits, and all ORGANIC which you did not cost a dime. 
Island life is different.  Island life is fun, easy and laid back.  Don't take your current life and compare it to what you will experience there.  You'd be surprised at how many expats and US students you meet there from many walks of life.  Americans, Europeans, Canadians.... Just come with an open mind, open heart and let the islands embrace you.
Good luck and I know if you do move to SKB you would absolutely love it.  Just remember to stay safe like you would anywhere.  The islands are a Paradise but crime happens in paradise as it does everywhere else.