If you're telling a story or presenting data on a map that is intended to be stylistically in sync with its subject matter, then building your own basemap is a way to achieve the look and feel you may be searching for. Using the ArcGIS Vector Tile Style Editor is the best way to customize an existing basemap layer available on ArcGIS Online, but you can also build your own basemap by just using feature layers and a little help from a reference layer.
Simplicity is key
Building your own basemap using feature layers works best for simple web maps and story maps that are not heavily focused on detailed location information like residential streets or building footprints. If all you need to see are countries and oceans, then the level of detail offered on many of the existing basemaps won't be necessary.
I recently made an ArcGIS Instant App called Home Run Heroes that showcases which Major League Baseball players have recorded the most home runs by their country of birth. In terms of a basemap, all I needed to show was world countries and oceans, but I wanted the map to look "baseball" in relation to the theme. Using following the datasets and techniques allowed me to achieve this.
The ArcGIS Living Atlas has a World Countries (Generalized) layer that I was able to use as my primary basemap layer. I wanted the countries to look like the dirt you would see along the base lines and pitching mound on a baseball field, so I chose a dirty, dark brown for their symbology fill. I wanted a chalk outline to resemble the base lines, so I chose a white outline with some transparency to give it a faded appearance. I made two copies of this same layer with no fill and just the white outline to form a halo around features with increasing transparency and outline width values. Labelling and map pop-ups are turned off since the only identifiable features are the points showing where each player is from. These layers are not visible in the map legend.
The Global Background is a handy feature layer that is also available on the ArcGIS Living Atlas. I was able to use this layer beneath the world countries as my ocean backdrop. I chose a dark, emerald green symbology fill to mimic green grass. Like the world countries, labelling and map pop-ups are turned off, and the layer is not visible in the map legend.
With those two feature layers in place, I was able to remove my web map's actual basemap layer by turning it off in the table of contents. The feature points showing where each player is from are symbolized by size with the larger circles representing a higher number of home runs. In addition to placing this layer at the top of my web map contents, a drop shadow effect was applied to make these points pop off the map since they are the sole focus for users to interact with.
To label the countries in a chalky, scrawly fashion, I leveraged the aforementioned ArcGIS Vector Tile Style Editor to create a reference layer showing only country names. I tried to match the country polygon outlines as best I could with white text and a light grey halo using the Walter Turncoat font style.
Lastly, I added a Watercolour Paper Texture overlay to give a bit of a rougher texture over the dirt and grass to make things seem a little more imperfect and naturalized.
The end result is a map that looks and feels like baseball. Play ball!