Well since nobody has responded I guess I will attempt to.
I've been brewing for 12 years and still learn something new every time I brew. This is because I like to try different ingredients or techniques with every brew and after 12 years I have yet to brew the same recipe more than 3 times.
Biggest challenge when starting.... finding a large enough pot and cooling the wort. Recipe and ingredients were no problem because as most newbies to this hobby I started out with a kit. Large pots seem to be more readily available now with Amazon and eBay so that should no longer be an issue for most people. Cooling on the other hand still takes time unless you spend a few extra bucks to get a cooling system of some sort.
The thing that got me in was the SWMBO got me a kit (Belgian Tripel), keg, Co2 tank, regulator, brew buckets, cleaner/sanitizer, hoses, taps, etc. for Christmas. She got me everything to brew and keg and bottle beer except the cooling and the brew kettle. Damn! I do have a good woman! She also got me the one resource that every newbie should read before they start .... The Complete Joy of Home Brewing by Charlie Papazian. It wasn't until I read it that I thought that brewing was something I could pull off. Actually had never thought about it before and before my first brew session the only experience I had with home brew was at a friend's house party. Someone brought their home brew.... worst beer I have ever had.
I choose recipes by ingredients I have on hand, beers that are getting good reviews and something I haven't had before. Usually when I go and get ingredients I need I will pick up extra items that I haven't used before and build a recipe from those ingredients. It forces me to learn and try something new.
The biggest challenges I see for new guys and gals trying this for the first time.... wading through the misinformation and taking the leap. Overall brewing a good beer is not that hard. With all the fully modified malts available hitting your temperatures and getting what you want from your brew session is not as hard as it once was. Starting out new people should use a tried and true recipe without trying to change anything. Should be done this way several times so you are comfortable hitting your temperatures and using your equipment. Find a friend that will be brutally honest with you about your results because not every brew is good and every brew needs to be judged objectively. You don't learn from smoke blown up your a$$.
The second biggest challenge .... patience. Time can cure what makes many beers off. Allow your yeast to do its job, use a secondary, cold crash, follow instructions until you can pick ingredients and brew without reading a book and then start creating your own recipes.
