Coffee hobbyist here. :)
Basically, you cannot make a latte with drip coffee, they are made with espresso (big difference), which you do need a machine for. There are many types of machines, but you generally get what you pay for. I could write you 40 pages worth of recommendations, but it depends on how much you want to spend, how much time you have to prepare it, if you want a grinder, etc.
It sounds like you enjoy sweet creamy "lattes" because they are made with milk rather than water (like drip), but you dont really like the coffee taste itself. Its also important to note that the milk in real lattes is not just heated, but it is stretched and steamed to produce microfoam, which is very difficult to make with anything less than 2% milk.
I guess its hard for me to suggest because Im not exactly clear about what you're going for..do you want coffee with flavoring and creamer or an espresso based latte with milk?
It all boils down to what you like though. Experiment with flavors, proportions, and strength. No one ever said you cant have a glass of white wine with a juicy steak if thats what you really enjoy. ;)
ETA: There is little difference between a latte and a cappuccino. They have the same ingredients (espresso, milk), but the difference is the proportion of steamed milk and milk foam (lattes have more steamed milk, less milk foam; cappas have less steamed milk, more milk foam).
If you're looking for something that has a less "bitter" flavor, I would suggest looking at other coffees. Good coffee does not have that over-extracted bitter flavor, but rather it has tasting notes and a nice smooth mouth-feel (like flavor notes in bottles of wine). When you are scouting coffee or espresso, keep in mind how fresh it is, the roast date, the actual roast (you may prefer a light roast), and the actual blend or single-origin bean (which part of the world it's from..they have different characteristics). We mail-order our coffee from Counter Culture based in NC, but we've tried many different roasters. I suggest checking out their website, you can get some great info there. I don't think they have flavored coffees though...
Since you asked, :) a lot goes into the art of coffee making. My husband and I have been hobbyists for years, doing everything from classes to roasting our own beans, to grinders and espresso machines, to latte art. It is definitely a science, but a rewarding one. We learned lots of basics from here: http://www.home-barista.com/. This website will keep you busy for days.