As a satellite technician, I think I can help answer some of your questions.
1. "I have also heard that some frequency bands are a lot better at cutting through cloud cover".
This is true. C-band has about 10dB less rainfade than Ku-band does, and Ku outperforms Ka-band as well (Not sure of the exact number as I don't do a lot of Ka links). C-band also requires larger dishes. You have to take into account what the acceptable availability is as well. 99% availability is quite possible and just requires a proper link budget (basically a series of calculations of gains and losses in the signal path which takes into account dish diameters/efficiencies, weather and satellite properties, among other things). Getting high reliability when taking into account weather is usually a lot easier on C-band, but if they are using an old bird with low output power or poor sensitivity, then a good Ku setup will outperform it.
2. "I would need at least 3/1Mbps with hopefully decent latency"
Latency is usually pretty fixed. The physics say it takes about 250ms for the signal to travel from your earth station to the satellite and back to the other earth station with an RTT of about 500ms. Any additional latencies are created by the FEC coders and access methods. The worst will probably be something that uses older Reed-Solomon over Viterbi (not used much anymore. Everyone has either already moved away from this 50 year old tech or is doing so right now) on a TDMA access system. I would expect an 850ms round trip time on this type of old system. The best will be a system that implements Turbo Product Coder or LDPC on an SCPC link (Dedicated link). I would expect about 600-650ms round trip. If you get on a shared network, anything modern will be using at least TPC and possibly LDPC if they're using DVB-S2 and you'll probably see an RTT of about 750ms (best guess on my part. each network is different). Additionally, using a shared access system will introduce jitter of which 50-100ms wouldn't be surprising to me. SCPC links tend to be quite good for lack of jitter. Getting the types of bandwidth you want is really a matter of contract.
3. "I've been looking for a decent contention service (4:1,10:1)"
On any shared access system, contention would be a matter of contract, and the lower the contention, the high the cost. When you start getting into 4:1 or better you're probably better off looking at a dedicated link, even if its not as fast as what the shared service is advertising. Personally, I'd actually rather pay for slower access with more generous transfer allowances than a fast connection with a really low transfer allowance. If you do go with a shared service, read their FAP carefully and calculate how much you can actually transfer taking into account transfer speed, FAP and transfer limits and compare this with your needs. It may also be to your benefit to either have multiple accounts with the same vendor or multiple vendors where you can switch between them as the month goes through. It could be cheaper than a more expensive link or cheaper than a dedicated link. Your budget will determine this.
4. Regarding "Globalstar, Iridium, Inmarsat, Thuraya and other similar systems"
These sorts of services will not provide the types of speeds you want and will cost you a small fortune in transfer fees, though they will have much lower latencies.
Unfortunately, satellite space is very expensive, as strider- indicated (and without sounding like we're colluding, I do know that he knows the industry). You really get into the "fast cheap reliable - pick two" and it should be more like "fast cheap reliable - pick one and hope for another one.... the third is right out" when you are dealing with some of the shared access satellite providers.