Assuming that it is okay for you to discharge the mixture into the drainage system, and that you have desirable soils (easy digging), and plenty of money, I recommend that you run a parallel line and bore into the manhole. I think this would be the most expensive of the options. The pros would be that your discharge will meet its destination each-and-every time. Another benefit is that you’re not impacting the existing storm drain’s capability. For instance, if the existing storm drain already runs full during a moderate rain storm, then you connect to it, you be interfering with the existing system..this may be a problem for the upstream land holder. To assure that you don’t interfere, you will need to quantify both the existing drainage flow conditions and the proposed conditions to assure there is adequate capacity in the existing line…this will require that a drainage study be completed, and this of course means more money.
If you have less-than-desirable soils (rocky, organics, weak fill), and choose to intersect the existing storm line because there will be less trenching, then connect to the existing line, but do so with a manhole. Manholes can be ordered in prefabricated sections, or can be built in the field (block type). Manholes aren’t very expensive, but will require additional construction time be undertaken as compared to the first option.
Placing a buried tee or wye is a risky idea. It’s highly probable that you will get a clog at the intersection at some point in time….unless, you are 100% certain that your discharge is free of debris and sediments, install a manhole. Some engineers may argue that you can install a cleanout or rodding inlet, but it seems to me that spending a little more money for a manhole is smart-money spent.
You will need to perform a costing exercise to determine the best choice for the situation. In regards to cost data, I would first speak to a local, reputable contractor to determine his pre-profit cost. If you don’t want to speak to a contractor, then RS Means is a popular publisher of cost data for construction. Beware: I've found their data to be inflated, laughable.
I hope this helps.
h.