Many of the older monitor calibrators were optimized for the general gamut of monitors of the period - sRGB or thereabouts and often don't perform well with wide gamut LCDs. You should be fine with the new models. The X-Rite seems to be the preferred device. If I were buying one today, that's what I would buy.
"I have seen both 1.8 and 2.2 as the preferred gamma for Mac systems. Does this setting depend on operating system and hardware? For my current set-up, is 1.8 the correct number? What about for Lightroom 3 on a Mac?"
It's been a long time since gamma 1.8 was recommended and even then it was usually for the wrong reasons. That really stems from a time before hardware calibration and profile aware applications where gamma 1.8 gave a closer match with black and white laser printers and with the default CMYK setups prior to Ps 5.0.
The native gamma of most monitors is in the 2.2-2.4 range, so calibrating to the 2.2 standard generally results in less of a correction being applied in the video card lookup tables, lessoning the potential for on screen posterization from too much a tweak to 8 bit monitor data. In addition, the most popular working color spaces are already gamma 2.2 or a derivative thereof and keeping your monitor at 2.2 helps when viewing non color managed web images.
So, the bottom line is that you should use gamma 2.2 whether on a Mac or PC, old or new. Colormunki is fine for your printer profiles.
I’m going to avoid #1, I’d toss the BlueEye (it was never that good).
2. The native TRC of most displays is in the neighborhood of 2.2. When calibrating a display, select 2.2 or if the software allows this option, Native. There is zero reason to move away from the native TRC gamma of a display with ICC aware applications. Doing so only adds banding to the previews. Outside non ICC aware applications, all bets are off anyway, so moving to 1.8 doesn’t really bring anything to the party.
The SpectraView II line is your best bang for the buck in a reference display (high bit panel, software that totally controls calibration attributes, control over contrast ratio, ability to build multiple targets for calibration and associated ICC profiles to switch on the fly).
3. The ColorMunki is a good device. If you want to build paper profiles great, but if not, just get the EyeOne Display-2 with custom filter matrices that NEC bundles with the display and its host software. This package only works on the NEC SpectraView II line. The Munki will do a fine job building profiles for the Epson.