You can upload your DNA files to:
Personally, I would not recommend using GEDmatch, due to the security issues with the service and their eagerness to undermine their own agreements with users. The data model that they use (anyone can look at the matches of any kit) potentially allows for anyone to extract your raw data from the site, and that is not a good thing for personal, family, or national security. Moreover, you can get segment data from other matches who upload to MyHeritage or FamilyTree DNA, both of which have better-for-privacy data models (i.e. you only see your own kit's DNA matches), so why not use them instead?
Of course, in both situations, you need to ask and persuade matches to upload to those services. That can be a major bottleneck. Hence my preference for 23andMe is due to segment data being immediately available (for those who have opted in), the ethnicity estimate, and also the comparisons that can be made.
Ancestry's most useful feature is that so many people have family trees. But it's only useful if you're willing to pay a monthly subscription to obtain full access to those trees. Non-subscribers can only see up to a person's 2nd great grandparents -- at best you'll ID 3rd cousins, but not any 4th cousins. And on top of that, only 28% of my top matches have trees - and many are rather small or not extensive. Not many people at 23andMe have family trees, though one can link to a FamilySearch tree for free. Let's hope that they allow for linking to WikiTree too eventually.
Let's consider an example. Steve has four DNA matches all descended from his 4th great grandfather: Alice, Bob, Calvin, and David. Alice and Bob are siblings. Calvin is 2nd cousins with Alice and Bob. David is descended from a different child of your 4th great grandfather, so he only matches 10 cM with Alice and 25 cM the others. Only David has a family tree, and it only goes back to his 3rd great grandparents.
Ancestry would show Steve his "Shared Matches" with Alice. It would just list Bob and Calvin with no additional information. But if these were on 23andMe, I would be able to see, immediately the probable relationships that I described above because 23andMe also tells me how much DNA Alice shares with each of her matches (the feature is called "relatives in common"). Additionally, because 23andMe has a lower "shared matches" threshold, Alice would also have David listed on her profile.
That kind of information allows one to quickly draw a sketch of what the family tree might or should look like, e.g.
So with Ancestry, you can probably build a little cluster of people (a number of people, including myself, do network graphs for this purpose), however with 23andMe, you can immediately work towards a good guess at your matches' relationships, without relying on them having an accessible tree.
With the 23andMe information, I can roughly sketch out what their tree should look like, and start asking specific questions via messages: "Hey, Alice, I think that we might be 5th cousins. Do you have a family tree? Are any of your ancestors from Texas? I was wondering if you know how you're related to Calvin or David? etc..."
Often, you'll end up having to do lots of family tree building on your own, in private. I sometimes add down to my matches' grandparents on WikiTree, which is part of why I'm pushing for a new mode for inviting users to join us.
23andMe also has a new feature that attempts to predict a user's family tree. Essentially, they can lay out the connections and you fill in the names. It's still in beta, so the functions aren't 100% done yet, but it's promising.
Ancestry's ethnicity estimate is essentially a map with percentages. 23andMe takes it a step further and kind of shows you their match behind it, by showing you exactly which parts of your DNA their model has concluded originated in each place. (see the pictures in this blog post)
Additionally, 23andMe will use your father's and grandfather's results to phase your DNA and your father's DNA, so your ethnicity will have a much higher accuracy compared to Ancestry. You can use that information to help narrow down the origins of a given match to try to see if a segment matches up with a particular ethnicity; that can sometimes help narrow down the search to figure out common ancestors.
One other note on why segment info from 23andMe is important: If your family has any kind of endogamous populations, it's essential to figuring out the true connection. Ancestry usually tells me the wrong ancestor pair for French Canadian DNA matches, since with most French Canadians, I usually share about 20+ common ancestors. Ancestry just picks the one where we've both spelled names the same who is closest to both users. (There's a note in the comments here about this.)
If you are ready and willing to either (A) subscribe and continue paying Ancestry or (B) try doing a network graph, Ancestry could still be useful, but I generally have found greater utility from 23andMe.