wad the 18-200 offers u is versatility. the 18-55 and 55-300 combi offers better IQ than 18-200 alone, plus longer reach. but 18-200 reduces the hassle of changing lenses, which is a plus point for traveling.
my advice to u:
ask urself, wad do u really need? versatility or low light + longer reach? or do u even need these at all? only u can ans this urself.
don't don't don't don't don't don't don't don't don't don't buy the 50 1.8 simply because if you are not used to manual focusing it is super hard to use and u'll mis-focus very often without the AF (d3100 has no internal focusing motor)
my 50 1.8 slept in the dry cabi for very long till i upgraded my cam body
18-200 and 35 1.8 should be a good choice imo for what you are doing
you might want to look at the photos you take, if most of them are at 18mm, then a wider lens might do you good. If most of them are at 55mm, then get a 55-200 to complement your kit lens. If you want more subject isolation from background blur then get the 35/1.8, not the 50/1.8 since it won't AF on your camera body.
You need to consider the type of photography you are into. With that, you will choose the suitable lens for the purpose.
If you are into wedding/ event, prime lens will be good but at times, you might need the zooms. However, you do not need zooms that goes beyond 105mm; in view that IQ will be affected in certain ways. Read more on portraits, or wedding photography, so that you will understand more of the type of equipments required. Many of the replies will only general share their views but not making you understand.
With D3100 (without in-camera AF motor), choose those lenses that come with AF motor; otherwise you will be doing manual focusing all the times (unless you are good at it, though manual focus is essential to master). So find out which lens has AF motor, & compare which lens will help in your shooting; then make the decision to buy.
Do not buy it, just becoz someone tell you how good or fantastic the lens is. Don't get contract the 'buying' virus & then regret with it where you might decide to sell them in the next few days or month. It's not worth as the price will be depreciated which means you will suffer a loss.
So instead of making a loss, why not make good use of your kit lens till it's fullest before you venture to the next better lens. By then, you would have master the basic shooting skills.
If you have a better budget, get a relatively good flashgun (SB-600 & below) with either a prime like 35 f1.8, or 18-105 (at 105, sharpness for portraiture will be good). Since one of your options is for 18-200 (which cost about $1,100+), why not get something which gives you IQ instead. Read up more on the Nikkor lenses.
Keep your 18-55VR, you won't regret doing so (trust me...been there, done that).
The above recommendation is more suitable to use with D3100 due to it's small body & the need to use when shooting wedding/ event.
Well, I will share this much for now. Hope the above will help you better understand what you really need.