Generally speaking, the latest publicly available version of the UO client is always preferable when connecting to a UOX3 shard.
In those cases where updates to the client are destructive for normal gameplay on your UOX3 shard, either because of changed client functionality or because it simply doesn't like UOX3, warnings will be posted in the forums not to run the UO patcher until those issues have been fixed.
Making a backup of your client.exe before any patching progress is, in any case, highly advisable.
Since UOX3 does not accept incoming connections from encrypted UO clients, you must find a way of removing the encryption from the client before you can login. To do that, you can use one of the many tools that exist for just this purpose.
ConnectUO is one such program, and is the one recommended for use with UO clients connecting to UOX3 shards. It removes the encryption at run-time only, and does not alter your default UO client permanently in any way.
Razor is another program you can use for this. It also includes a lot of bonus features that can make playing less of a hassle.
After downloading and installing ConnectUO, start it up. You will be greeted by a download bar - worry not, that is just ConnectUO retrieving the latest updates and/or list of privately run UO shards.
Once the download is finished and ConnectUO is started, click on the link named "Local Servers" in the "Server Lists"-menu on the left. Now click "Add Local Server" near the top of the ConnectUO-window. Enter a name for your shard (visible to yourself only, so doesn't matter what you write), as well as a description if you feel like it - before moving on to the important part.
Under "Host Address" you must enter the IP-address to your UOX3 shard. If your UO client is situated on the same computer as your UOX3 shard, enter 127.0.0.1 as the IP. If the UOX3 shard is on a different computer, for instance on your LAN or even on the Internet, enter the LAN/Internet-IP for the shard instead. In all cases, set the "Port" address to 2593, unless you have specifically changed that in UOX.INI.
Also make sure the "Patch client encryption" checkbox is enabled. When done making all the changes, click the "Add"-button to add your shard to your ConnectUO list of favourite shards.
On the "Local Servers"-page in ConnectUO, you should now see your shard listed. To launch the UO client, simply click on the "Play"-link next to your shard-name, and ConnectUO will automatically remove the encryption from the client as well as configure it for logging onto your specified shard.
After downloading and installing Razor, start it up. You will be greeted by a welcome screen. Leave "Load Client:" on "2D Client (Auto Detect" unless you encounter a problem with auto-detecting the client, or you have multiple clients installed. Make sure the "Patch client encryption" flag is checked, then enter the IP and port of your UOX3 shard. If you're running the UO client on the same computer as your UOX3 shard, enter 127.0.0.1 as IP and 2593 as port.
Once you've completed the initial setup of Razor, click on the Okay button to launch the UO client. You should now be ready to log onto your UOX3 server by entering the username and password you specified during the UOX3 setup process.
Razor also includes a whole host of extra options you can enable or disable as you see fit.
When the UO client has loaded, type in the username and password which you specified during the Installation/Configuration-process for UOX3, and you should be good to go!
One thing you might notice when you log in for the first time, is that your world is void of any Non-Player Characters (NPCs) as well as any decorative/usable items. You can fix this by either populating your world manually, or by downloading premade spawn and/or worldfiles from the UOX3 Downloads-page.
For more information on how to run/administer your shard, check out the following pages:
UOX3 Server-Settings (Local copy)
UOX3 Command List (Local copy)
Xuri's UOX3 Guide (External link)