I recommend all synthetics to the maximum extent possible. Cotton has a ton of weaknesses, it wrinkles, it stains, it dries slowly, it stretches and loses it's shape, it's heavy and bulky to pack. It does have one notable benefit, it breaths well (which can be nice in hot weather). In the backpacking world, people say "cotton kills" because it loses all insulation when it gets wet.
I really like underarmour boxer jocks now. I also have similar made by Adidas. I prefer a fly and longer inseam to keep them from riding up. They wash in the sink well and dry overnight, quicker if you ring them well.
Cotton socks lose their insulation if they get sweaty, which opens the door to blisters. I look at fabrics and buy something with no cotton in it - right now I have Puma and Underarmour crew socks (black) that work and Calvin Klein dress socks (also black) plus some Puma no show socks that aren't cotton. I have wool hiking socks too, but I wouldn't pack them for Greece; I'm more likely to pack the no-show socks.
My favorite pants for travel are golf pants. They're light weight for packing, comfortable in the heat and look nice enough to wear as slacks. I've paid up to $80 for Adidas but I've seen many brands on sale this time of year.
You can get hybrid shorts at Costco for $12. They're built to be walking shorts or swim shorts and aren't cotton.
For t-shirts I usually pack Adidas ultimate tees or similar by Underarmour. I find some perform better in the heat than others, so I pack those in warm months. Most of my closet is stocked with clothes that include travel as an option, so I'm just grabbing a few of my favorites.
For button up shirts, I've recently started buying Ex-Officio. I thought they were too expensive but they opened a Sierra Outfitters in my area and their price is reasonable. My selection of button up travel shirts in my closet includes a couple from North Face, a couple from Columbia and a couple of Ex-Officio. I'll just pick a couple from those that mix and match with what I'm packing. I rarely wear a polo or golf-shirt when I travel. If I did, I have a selection of non-cotton choices in my closet.
I really think it's worthwhile to try them out at home. Some of the newer synthetics perform surprisingly well in heat and cold, but I can't say it's true of every item - even the new ones. They all have the advantage of packing light and wrinkle free, washing and drying easily and staining much less than their cotton counterparts.