I guess the hard truth is that the best way to satisfy your desire to fill as close as possible to the target price is to determine the right target price (and order size). It should be realistic while maintaining probabilistic benefit for your trading routine. Learn your stock's trading volumes and buy/ask spread for the start. The effective spread is the price range where any price targets are meaningful most of the time. Understand that the highest chance of your order executing is when the price is closer to the unfavorable end of the spread, and when your order size is reasonably small to get absorbed by the other side of the trade before the spread moves in unfavorable direction.
Generally speaking there is zero guarantee that the stock you are interested in will ever trade at the price you consider beneficial, and there is almost zero order types that are guaranteed to execute at any price. With market orders you have to accept insurmountable slippage?tendency of the target price, and with limit orders you have to accept longer times and higher uncertainty of execution. Therefore try to learn what you trade and plan accordingly.
That said, generally speaking small marketable orders in highly liquid stocks tend to execute very close to the last trade price, especially approaching market closing time when trading volumes are at their highest and spreads are smallest. Your asking these questions suggests to me you are trying to trade illiquid stocks, or placing very large orders, which together with poor understanding of the problem can make your trading somewhat prone to some funky mistakes.
These questions are actually not only beyond the scope of this forum but indeed one of the most complicated problems of the market and business in general. Market makers make their living by putting the science of it into action on the supply side.
In respect to the technicalities, TriggerMethod property is not used for market or limit orders; it's just for stops. You can try tinkering with SMART routing execution preferences in TWS configuration but it will get you only so far. I believe there's really no substitute for determining the right price and size of the order.
