There have recently been significant changes to the immigration rules for entry to the UK for non-EU migrants, and even more stringent measures are anticipated regulating entry of non-EU migrants in the near future.
The Points Based System is now the main system for people applying to live and work in the UK from outside the EU. There are different "Tiers" applying to different types of migrant worker, so you have to apply for a visa under the correct Tier. There used to be many more categories but they have all been recently streamlined to restrict numbers of entry.
Tier 2 is for Skilled Workers who have a job and a sponsor (the employer) and are coming to fill a position which cannot be filled by a settled worker. The only way you can apply/succeed under this Tier is if you find a job before coming, and to be honest, unless you are in a particularly niche area of the job market, or willing to work for very low pay, it is unlikely that coming from the US, you will find a job that cannot be filled by a settled worker in the UK. So whilst I would advise you to do your best looking for a job whilst you are still in your country, I wouldn't pin my hopes on obtaining a job/visa under Tier 2.
Alternatively, and most likely, you will need to apply under Tier 1 of the PBS which is for highly skilled migrants, investors, entrepreneurs and graduates of UK universities. You do not need to have a job to apply for a visa under this Tier, which means that if you apply and are granted a visa, you can come and live and look for work (or not) and take your time looking once you are here.
I'm guessing you are neither an entrepreneur (in the strict sense), an investor or a graduate from a UK university. In which case, you can only apply with any chance of success under the Tier 1 (General) which requires you to be highly skilled, with good English and with enough money to support yourself. Basically, on the basis of information in your application, you are awarded "points"....so everything from your age, whether you have a degree, what jobs you have had in the past and other experience, how much you have earnt in the past, language skills and funds etc....they all attract points. The more "highly skilled" you appear to be, the more points you get. You need a certain total of points for entry into the UK: 75 to be exact.
You get 20 points for age up to 29; 10 points if 30 and over
You get 10 points for English language proficiency
You get a grade of points depending on whether you have an MBA/PhD/Masters/Bachelors degree from 75 points to 30 points. You get 0 if you have none of these.
You must have at least £2,800 funds to support yourself and have no recourse to public funds: you get 10 points for meeting this maintenance requirement but if you don't have it, you can't get a visa even if you have over 75 points.
You also get points for previous earnings and previous earnings in the UK. This ranges from 75 points if you've earned £150,000 in the last 12-15 months, on a scale down to 0 points if you have earned less than £25,000 in the last 12-15 months.
You could consider coming here on a visit/holiday: you wouldnt need to obtain a visa. You could then work hard at finding a job, and apply for the Tier 1 visa from inside the country, or once you find a job, apply for the Tier 2/Employer Sponsored Visa. Failing that, you could spend a couple of months really experiencing life in the UK to determine the ins and outs of living here.
Re the NHS, you can access the NHS if you are legally living in the UK (indefinite leave, with a Tier 1 visa, or some other means of legal residence) but you may not access other "public funds" for a period of time.
I think that the cultural side is one part of moving abroad...it's the logistics and the actual planning about what you're going to do here that is important. How are you going to live? Can you afford to live here now or do you need to save for a while? Rent in London is expensive, and if you don't have a job when you first arrive, you'll need to find a way to pay for that. As for work...there is work in the beauty industry, but there isn't exactly a shortage of beauty consultants/makeup artists in the industry. Your best bet would be to join a brand and then work at moving within the industry or going freelance. But it's all about contacts...and you'll need to build them up before going freelance I guess.
Maybe you don't want to be in London? Have you thought about where exactly in the country you want to go? Looked at cost of living etc...?