Just start experimenting and mixing all kindsa stuff, that's what I do.
My favorites involve mixing fruits with veggies.
Apple/celery and apple/carrot are really good.
If you make anything with peaches I'd combine it with another fruit that isn't as sweet. Pure fresh peach juice is EXTREMELY and overpoweringly sweet, so unless you like that, use less peach juice with more mellow fruit. I'd think a peach and papaya mix would be pretty good. Grapes mixed with peaches and other fruits might work well because most varieties grapes are tart enough to kind of tone down some of the sweetness.
Pears are good mixed with just about anything.
Carrots are a good veggie to add to just about any juice you make because carrot juice is so sweet. Celery adds a bite to anything.
Tomatoes work well in lots of mixes, but don't juice very good in a conventional electric juicer.
What kind of juicer did you get? Oranges and any citrus-like fruit doesn't juice very well in a normal electric juicer either, but I always just use a citrus juicer and then add the juices together. Btw, peach juice will come out VERY pulpy in this type of juicer, you may have to strain the juice before juicing anything else into it.