I can't give advice on booking package holidays, as it's not something I do much of. When it comes to booking flights (and hotels/rental cars/trains etc), however, I have quite a bit of experience. We currently have thirteen flights booked - maybe I should book one more to avoid the unlucky number?!
None of these are for our honeymoon, but some of the places we're going (Fiji, San Francisco) would be great honeymoon destinations. Some are with multinational airline alliances (BA/Qantas/One World), and some are with budget airlines. I'll fly with almost anyone, as long as the price and the time is right. The exception to this (apologies to those of you in the US) is some of the American airlines. We're flying BA as the alternative was United, who have consistently failed to deliver. Having said that, I was also unimpressed with Emirates, and they tend to get good reviews. On the flip side, I've yet to have a really bad experience on a budget airline - obviously you get what you pay for, but what do you really need on a 2 hour flight?
Budget airlines get notoriously bad press, either for being late (tight schedules) or for sneaky charges. Whilst the charges are annoying, just play the game and they can be minimised (check in online, take only carry-on luggage and pay by debit card). NZ's budget airline JetStar does much better than EasyJet or Ryan Air for the latter - you can pay by internet banking which is fee-free. It works really well for flights originating in NZ, but I've just discovered that it doesn't work for flights originating elsewhere as you have to pay in the currency local to where your journey begins.
Enter Expedia. I often read reviews of new flight comparison websites, but none of them seem to work as well as Expedia. I've used them since 2002, and although I shop around every time I book a flight, over 50% are booked through Expedia. They don't charge fees, have consistently good prices, good customer service and an easy to navigate site. This time they have even managed to trump budget airline JetStar on their own prices!
They're also great for hotels, and link in to Trip Advisor's rating system. I've used expedia.com, expedia.co.uk (you can spend and receive nectar points here) and expedia.co.nz, and can highly recommend them. And before anyone asks, they haven't paid me to say this!