Okay, let me summarise the flurry of links to everyone's favourite HUDs to the best of my ability. I haven't tried all of these individually, but I have seen most of them either via screenshots or POV demos. Either way, you should take a look at screenshots of each of them and try the ones that interest you the most.

I think it's pretty safe to say that if it's your first foray away from the default HUD, or if you're still learning the game, FrankenHUD is your best choice. Think of it like the default HUD+; it's the most visually similar to the default so you'll have a minimal adjustment period. However, FrankenHUD emphasises things you need to see (such as your health, ammo and recharge bars) while letting less important things fade into the background. I'd even recommend FrankenHUD to new players, as it doesn't outright hide anything and isn't confusing for those still grasping the feel of the game.

Next step up is something along the lines of eveHUD. EveHUD is a little bit harder to read for someone that doesn't know most of what's going on, and it has a bit more flair to it than FrankenHUD. However eveHUD dramatically increases the size - and hence readability - of health, ammo and recharge meters and does away with most of the fancy - but useless - backgrounds on HUD elements. I'm not a big fan of some of the menus, but it's otherwise extremely solid.

Now we're getting into the realm of minimalistic HUDs; these excel in only delivering you critical information, thus freeing up your screen to see more, but don't offer much by way of explanation of what the HUD elements actually mean; it's assumed you already know what they're for and what they mean. So without further ado:

First port of call is the CommunityHUD (CommHUD for short). (A slightly modified version of) this HUD is used by eXtv and Salamancer for casts and is a solid gameplay HUD. Health numbers, Ammo and recharge bars are HUGE making them extremely easy to read at a glance without being intrusive. Being a minimalistic HUD, it lacks a lot of explanations (eg recharge bars don't tell you what they're for) and most non-vital notifications are hidden completely (eg the "That was impressive!" panel during respawn). The only downside is that it has become rough around the edges as the developer (Flame) has committed less and less into minor - but important - bugfixes. I personally use CommHUD with a some self-written fixes and some elements from other HUDs.

Next is PVHUD. It's similar to CommHUD (the latter was somewhat based off the former), but even more minimalistic. The menus are heavily simplified in terms of looks (most menus are no more than text lists in some places) and some spacings are different. PVHUD is a love-it-or-hate-it kind of HUD. On one hand, people love the simplified menus and some of the extra features like a separate updater (it's one of - if not the only - HUD which has this). But if you're like me, I find the menus too difficult to read and they ruin the aesthetic of the game somewhat. If you don't mind that, it might be for you.

Then there's RevanXP-HUD. Again, along the vein of CommHUD and PVHUD, but it uses a different font from the default and all previous HUDs (TF2Build, IIRC) for most of its HUD elements. Additionally, it centers several HUD elements (such as the medic's übercharge) which may be good or bad, depending on your preference. I may be easier to read, but I personally think placing permanent HUD elements near the crosshair causes them to just get in the way.

Also, we have GarmenHUD. Another love-it-or-hate-it, this HUD uses a radically different font which can be hard to read at some times, but does a few things very well, most notably the colour of your health changes when you're low and overhealed. I'd at least try it to see if you its benefits and drawbacks are right for you.

There are several others that people have linked to here, but I will say now that I haven't had enough exposure to these to make a full comment. Also I'm running out of post space.

TL;DR: The first paragraph, then skim the links.