I would like to have my family tree online to share with relatives. I do not see a current need to have any extra such as matches with other people's trees and resources (online sources).
Would I be better to publish using one of my software to a free web account, purchase a domain name and publish or use one of the genealogy sites?
If you want to share your information with relatives in a format of your choice, then your own domain will allow you most control over what to publish and how to present it. There are a wide range of options for creating this and controlling access to it, depending on the facilities in any software you're using to record your family tree and your own confidence with the various technologies involved. If you give us a little more information about that, we can make more specific suggestions.
One advantage of using your own domain is that it makes it (a little) harder for others to copy your work without permission — depending on how you set it up, they may actually have to go to the trouble of re-entering all your data rather than copying it with a couple of mouse clicks. (Of course, this may not matter to you.)
If the software you use has a user group, you may find that there's a gallery of members' websites that will give you ideas about what you can achieve.
You say you don't see the need for "matches" at present, but I will say that I've made a number of contacts with unknown cousins using my own domain; many researchers include as a matter of course Googling (or the equivalent) for persons of interest.
Use of the free facilities at Ancestry would be a simpler way forward in one way — you have no control over appearance, so you don't have to make any decisions about what or how to publish, other than removing information about living people and any other private or sensitive data, just as you would with your own website. (There's some useful discussion of this topic at What information should or can I publish to a web site?.)
With Ancestry, you can control who can view the tree, from restricting it just to people you authorise to allowing unrestricted access. Your relatives may not find it convenient to set up an (free) account with Ancestry, which they will need if you chose to restrict access.
Ancestry is a good source of contacts with unknown cousins, but makes it very easy for them to copy your work without permission once they have access to your tree.
If you were interested in "matches" I would recommend you take both approaches — your own website, that looks the way you want it to look, and is easy for your known relatives to access, and Ancestry (or a similar provider) to maximise the chances of finding unknown cousins. As you don't care about matches, your own website is probably a better fit for what you want.
If you are interested in finding distant relatives, I recommend uploading a version of your tree to ancestry.com. It's free to do this (you only need a paid subscription if you're going to use their search service), you have control over what gets put up, you can control whether your tree is findable but private, or public, and you have a reasonable chance being found given the largish number of users of that site.
What you don't have control over is how your tree looks to others -- every tree looks the same. If you're more interested in having a specific look and feel, and your goal is to share your info with your family, then probably a personal site will be better, particularly if you like tinkering with html :-)
Another option, if your goal is to have your family contribute to your tree, is to create a tree on Geni. The downside of this option is that anyone whom you give the permission to edit information can enter wrong information. Also, this service now costs money.
There are, of course, other genealogical sites for other purposes, as other answers will doubtless show. If you modify your question to make your goals more explicit, that will help make the answers more pertinent.
It depends on why you are publishing the information.
Is it for vanity? Is it for sharing with other researchers who may be connected? Is it for sharing with relatives? Etc etc. Depending on what it is for would shape different answers.
My initial thoughts are if you want to put a limited amount of information online then you would be better with your own domain and site or a free host. If, however, you want to share with a wider audience then one of the genealogy sites would be a better bet.
Be aware that you may not get much contact from others through any type of web publishing.
{substantially edited} I have had a similar need: to share trees with images and biographies -- subscription-free. In principle, the research, data entry and design of your tree is a separate thing from its sharing for viewing purposes. The online sites are good at the former but not the latter because they rarely have a separate, subscription-free interface for non-members (my family do not want the complexity and cost of such sites).
I had to develop a custom tool to design trees that could be shared via websites or even blogs. That tool is now free for all to use: SVG Family-Tree Generator (6.0). It allows you to graphically (i.e. with a mouse) lay it out the way you want it, and enter historical or biographical details, and images. It also supports GEDCOM so you can publish a tree that you have already created elsewhere. An important feature is that these trees are interactive, and there are several packaged applications that you can add to them, ranging from simple image or biography manipulation to timeline reports and hyperlinked trees. The design tool is Windows-based but the output works in all modern browsers. The above article mentions an installation kit, documentation, samples, and a Facebook group with instructional videos.
Contrary to others, I recommend AGAINST ancestry.com.
There have been many complaints of them "not receiving" cancel instructions for the "free" trial that actually requires a payment method to start it.
Furthermore, they put out a lot of click-bait that only leads to a sign-up for their "free" trial.
Their corruption of the GEDCOM format is horrible.
And worst of all, they offer lots of recommendations for people who don't know better to add false information to their trees.
I recommend publishing directly to a hosted website under your control using one of the truly free software packages. My favorite is webtrees, but I believe GRAMPS and others also exist.
Like others, I find Ancestry is excessively interested in selling enough DNA kits to pay for their incessant TV adverts.
After trying a couple of other websites, I use Wikitree. This is free to use, both to post your tree and to search other trees.
You can set up a level of privacy to suit your requirements.
As some others have mentioned, there are specifics that would make it easier to offer 'tailored' advice / options (with regard to software, custom websites, privatized (or not) coding...) but from someone who actively works on multiple public sites like Ancestry, WikiTree, FamilySearch, GEDmatch etc there isn't much else to add with regard to the pro's and cons of having your own domain and putting your tree on Ancestry as those options have been thoroughly described.
If you choose Ancestry you can now (May 2022) keep an active tree set to any privacy level with the ability to edit and add new information without paying any type of fees or renewal.
I still see "hints" for relatives but
I wanted to offer a few sites you would want to stay away from if keeping your tree "as is" and unable to be edited by others. WikiTree and FamilySearch are two of my favourite websites to research and edit but they each share a premise to have a large, single family tree which will theoretically unite everyone so uploading individual trees only complicates their processes and your goals. For example, any profile for an ancestor who already has a profile on the site would be "merged" with the original and you wouldn't have exclusive control over data edited.
