I would say, first of all, kudos to you for working out at 349 pounds - I don't know many people at that weight who can do the amount you said you do.
I spend a good deal of time lurking around these forums and there is a lot of specific advice but in the end, it kind of all boils down to one thing: the best amount of exercise is the amount that you can do and stick to without getting burned out or injured and giving up. And I do agree that it's probably a much better idea to start slow and work up to doing more than to jump in and overdo it starting out.
I actually have a similar schedule to yours. I lift weights (focusing on my upper body) on monday, wednesday, and friday, and it usually takes me about 45 minutes to complete my routine. On tuesday and thursday I do cardio intervals, and I am done well before a half hour is up, so I do a few squats and lunges after that. IF I feel like working out on the weekend I usually do more leg stuff to even out the schedule a bit.
If your schedule is working for you, i.e. it makes you feel good, you can tell you feel healthier, etc., then by all means it is okay. Once you get good enough at what you are doing, you will find you can slowly increase the duration (or intensity, if you prefer) of your exercise to keep making progress.
As for working specific muscle groups versus full body, that's up to you as well, however I would try to at least do a full upper body or full lower body workout at once as opposed to, say, only working your biceps and triceps in one workout, because you would be missing out on a lot of strength building and calorie burning if you only work two muscle groups at once.
Again though, I'd say based on what you said that you're doing pretty well. If it's working for you, then go for it