Concerning the Ohms question, headphones have a very wide range of impedance levels. Some require a ton of current to perform properly, whilst others can get by fine on what an iPod gives you through the audio jack. The determining force at work is impedance, measured in Ohms. If you're dealing with HD600s @ 300 Ohms or DT880s @ 600 Ohms then they won't receive the current to perform properly without good amplification, and the effect will be low volumes and dead dynamics. Contrasting this, the Beyer Custom One Pros @ 16 Ohms will pair fine without an amplifier. You then have examples such as the AKG K 702 @ 62 Ohms which can be a pain to pair correctly.
Getting onto the mixing - before I mention the negatives, I'll readily say that mixing on headphones is possible and can be almost as good as monitors in a treated room. But there are a lot of aspects that must be trained, honed and mastered, and you'll likely need to invest heavily on getting what you need if you aren't prepared to work on principled compromises to how things sound through more modest setups. I should also say that I am working on the assumption of an eventual high level of quality, backed with ability. If that isn't the goal, then all this can be toned down a lot.
If you're mixing with headphones instead of speakers, then you may be held back considerably by any headphones that don't possess a markedly flat frequency response. This is because many headphones will colour the sound for a consumer's taste, not the person making the music. Worse still, your spatial sense of the aggregate sound will rarely apply to headphone mixes, almost certainly leaving the mixes heavily coloured through specific frequencies and it may well sound amateur or strange. The Beyer Custom One sound like they will probably get you caught in the trap of underwhelming lows, overwhelming peaks in the mids and slightly aggressive highs, if you simply mix to them by ear alone. It's also extremely important to understand that headphones magnify details in a track - so when you've loaded up your VST like Sylenth or Massive and finely tuned a lush, sparkly pad, you'll be pretty sad when you realise that next to nothing of the finely tuned detail is translated through speakers, and that other headphones aren't anywhere near as kind to that sound as you'd like.
If money isn't an issue or you are serious enough to invest heavily, I'd strongly recommend getting a monitor setup alongside multiple headphones. I almost exclusively use headphones for mixing, and my current rotation is based on the Focal Spirit Professional (flat, closed-back circumaural), AKG K702 (flat, open-back circumaural) and a pair of Sony MDR-7506 and Sennheiser earphones to check how consumer devices should likely sound. This is a really important step that a lot of people don't do. I will still deal with lower frequencies primarily on the monitor setup, and I wouldn't recommend trusting any headphones unless you've gotten a keen insight into how a particular pair translates to particular monitors. I've also just got the Phonitor 2 which I'd recommend to anyone with the budget for it. This saves a ton of headaches.
Granted, if you're just starting out then it is silly to assume you will need to invest so heavily, and it is even more silly to expect good results immediately. It takes a lot of exposure, a lot of practice and a lot of effort to bring all the elements together into good practice and form.