Using footage with different container formats

Sorry if this has been answered before. I did a preliminary search and nothing came up. I was wondering what professionals do when they need to edit a project in which the 'dailies' consist of media encompassing multiple container formats, say for a client's demo reel. This is my situation actually. A client has only digital copies of their work. They are all encoded differently. I'm fairly new to freelancing and I guess I got lucky because all my previous clients either had DVD copies allowing me to rip consistently or little variation in digital container formats.

In previous cases where I've worked with 2 different formats for the same sequence, I didn't give it a second thought--I layed my footage down, cut, and exported with no hitch. I'm assuming that I won't have a problem working with the footage, but I would just like to know if there are any precautions or unintended consequences I should be aware of for using footage from sources with varying containers.

Is quality lost/inconsistent? Should I be transcoding the footage myself in some lossless format so that the containers are congruent throughout? This suggestion makes sense to me as you'd ideally want RAW/lossless formats to begin with but when transcoding, for example, an MPEG4 into a lossless format doesn't it just retain the same quality if not worsen? Do most encoders (say adobe media encoder, super, AVID's native, or handbrake for example) treat footage that originated from different media containers differently? What do pros do in terms of varying aspect ratios across footage (16:9 with 4:3 or 3:2)? Combining HD with SD? I'm sorry I know I'm throwing a lot of questions out there but I guess I am just looking for more information on the subject. Mainly, I want to know if it matters at all and in what ways!

Any help will be appreciated! Thanks!

- Zak