If you want to use EL84s as output tubes . . . they're a good candidate for traditional Ultralinear loading, operating class-AB1 with cathode bias - you'll get a solid ten watts with very respectable distortion.
Choice of driver tubes of course depends on the driver circuit topology - you could do it Dyna-style with a pentode driving a split-load phase inverter . . . look at a schematic for a ST-35.
Personally, although I'm a Dyna fan . . . I prefer a long-tailed-pair phase inverter, and it's really hard to improve on a well-implemented 12AX7 or 12AT7 in such an application. For an input tube, if you wanted high loop gain, then an EF86 pentode would work great, and what you end up with is basically a Mullard 5-10 circuit. But for a modern amp (especially if driven from an active preamp), then the gain is not as necessary, so I'd probably use a plain ol' 12AX7, and share it between the both channels. There's a good reason why the 12AX7 is so ubiquitous . . . if correctly implemented, it kicks butt, and it's a reasonable assumption that they will be easily available long after we're all dead.
No matter what you choose, I'm a big advocate of well-implemented feedback amplifiers, and with EL84s, there's no reason why you should need more than two driver stages, and the input stage should be DC coupled to the phase-splitter for minimum phase shift. If well designed, a traditional EL84 amplifier can be of reasonable size and price, good stability, long tube life, good speaker compatability, zero maintainance, low distortion, and very good sound quality.