Long gone are the days where ASCII was enough for everyone. Long gone are the days where you can deal with strings with no "weird" or "funny" characters.
I became a developer in a time when the only encoding we had was ASCII. You could encode all strings in sequences of bytes, 'cause all characters you could use where encoded from 1 to 255 (well, from 32 [space] to 93 [close brackets] and you still have a few latin-accented characters in some higher positions, although not all accents where there).
Today, accepting characters beyond that is not the exception, but the norm. To cope with all that, we have things like Unicode and UTF-8 for encoding that in reasonable memory space (UTF-16 is also a good option here, but that would depend on your language).
So, as much as you to make your system simple, you will have to keep the internal representation of your strings in UTF-8/UTF-16. You may not receive the data as UTF-8/UTF-16, but you'll have to encode it and keep transmitting it around as UTF-8/UTF-16 till you have to display it, at which point you'll convert from UTF-8/UTF-16 to whatever your display supports (maybe it even supports displaying in UTF-8/UTF-16, so you're good already).
Today, I believe most languages do support UTF-8, which is great. You may still have problems with inputs coming from other systems that are not UTF-8 (old Windows versions, for example), but that's fairly easy to convert -- the hard part is figuring out the input encoding, though. Also, most developers tend to ignore this and assume the input is in ASCII, or ignore the input encoding and get a bunch of weird characters on their printing, 'cause they completely ignored the conversion on the output point. That's why I'm repeating the mantra of UTF-8: To remind you to always capture your input, encode it in UTF-8 and then convert in the output.
One thing to keep in mind is that UTF-8 is not a "cost free" encoding as ASCII: While in ASCII to move to the 10th character, you'd just jump 10 bytes from the start of the string, with UTF-8 you can't, due some characters being encoded as two or more bytes (you should read the Wikipedia page; the encoding is pretty simple and makes a lot of sense) and, due this, you can't simply jump 10 characters 'cause you may end up in second byte that represents a single character. Walking through the whole string would require traversing the string character by character, instead of simply jumping straight to the proper position. But that's a price worth paying, in the long run.