PHI is a good company. Air Logistics and Bristow are one and the same (one being a subsidiary of the other; the company operates in the GOM under the Air Logistics name). They are also a good company. Another large GOM operator is TexEra. They are the result of what used to be two decent companies but it seems two plus two didn't add up to four when it comes to working conditions. These large companies tend to have the better pay and benefits packages (somewhere on the order of $50,000 to start, with medical/dental etc.).
Then there are the smaller companies like RLC. Pay and benefits may not be as good but the lines of communication should be pretty short, which some people prefer. Maintenance ranges from excellent (all the large companies) to 'meets the regulations' (some of the smaller ones). None of these companies have an unblemished safety record. Having said that, the larger companies will likely employ a more scientific, institutionalized approach to safety and will have more resources to do so.
By the way, you'll need a work permit to be eligible for employment with any of them.