First, if you decide to handle it yourself (i.e. pulling out the chainsaw): please — please be careful. There are plenty of chainsaw safety videos online, and it is worth watching them. Here is one that an arborist friend recommended to me after my husband nearly severed his leg a few years ago fixing another downed tree problem.
Know that having someone else come in to deal with the problem is not going to be cheap, but there are ways to cut costs and perhaps even end up with some nice materials. If you have space, you can often get a price cut if you can deal with the wood yourself. Do you have a wood burning stove? Is the wood burnable (if it is dried)? Maybe you can have the tree chipped and then you can use the chips in your garden or compost pile. Maybe you can burn branches later in the winter — an outdoor firepit might need some fuel. Anything you can do to make lighter work and less to haul away will save dollars and cents.
Our tree came out by the roots, which poses a whole different set of troubles than a tree that broke and fell. The stump, if it is still in the ground, will likely be a problem to work around once the tree is gone. Stump grinding is a great option for getting the stump out of the ground (particularly if it is a large tree). I have found that grinding is priced by the stump and the more you have the cheaper it gets. If you only have a few trees it might be worth combining with neighbors who have also lost trees to get the grinder in together. You will all save money over each of you hiring separately.
If the tree has come out by the roots the best thing to do is to get it cut down to manageable sizes that can be chipped, burned or otherwise used. Do not, as I have seen and heard people do, dig a big hole and bury the stump. In many areas this is illegal as it can pollute groundwater, and it will likely cause sinkholes later.
And finally, if you want or need to replace the tree, make sure you consider why it failed in the first place. Was it a Bradford pear that just split and fell? It is worth knowing that this will likely happen to a future Bradford pear as well. It is a common characteristic of the tree. Many trees have distinct characteristics that might make them terrible choices. Perhaps it fell because it didn't have enough space to grow properly and was subsequently top heavy or straggly. If that is the case, it would be worth opting instead for a smaller tree. Of course, in major storms it is certainly conceivable that a perfectly healthy and perfectly placed tree just came down because of obvious forces of nature, but make sure that is really the reason and that in replacing it, planting conditions haven't changed, making something else a better option.
(Image: Rochelle Greayer)