What are some good strength training options for someone just starting out? Specifically related to building a solid foundation of strength across all major muscle groups.
Two of the programs with a lot of following are Starting Strength (website / book) and Strong Lifts 5x5 (website). Whichever program you follow, the Starting Strength book is worth its weight in gold.
Once you get into the intermediate phase of strength (again, as defined by strength standards), you can look into other routines designed for trainees at that level (Texas, Madcow, 5/3/1, Westside, etc). Don't be eager to jump from novice to intermediate: progress slows down the stronger you get. Leaving a novice program that you are making solid progress on to move to an intermediate program will slow down your overall increases.
If you don't have access to a gym, consider a body weight program. If you go that route, consider a suspension trainer or (harder) a pair of gymnast rings. Also, a couple of kettlebells can take you far. These options won't be anywhere near as effective compared to a progressive barbell program, but certainly better than nothing.
The most important element of any program is that it meets you where you are.
If you're somewhat athletic and without major mobility problems, Starting Strength and 5/3/1 are two good choices among many. The key element here, in my opinion, is to avoid unnecessary aspects of bodybuilding, to develop consistency, and to work towards mastery of basic movements like squatting, bending forward, pushing, and pulling.
If you're not very athletic, then something like StrongLifts (which is essentially Starting Strength but with less explanation of the lifts, starting with lighter weights, and progressing more slowly) or stumptuous' Less Thinking More Doing starter program. Programs that are more general (as in, not purely strength-focused) or that introduce more exercises are often quite useful with people at this level. Ross Enamait's programs are good examples of this kind of strength-biased general program that involves substantial exercise variety.
If you're extremely unathletic or have chronic trouble with joints or mobility, or if you're not ready for a standard-issue program for whatever reason, then physical therapy or a specialized program designed in person by someone experienced is necessary.
Meeting the beginner where they are is the hardest and most important part of choosing a program. The goal is to find a program that addresses training goals in the most efficient and rational manner. Since goals and people's abilities vary widely, the possible best programs are innumerably many.