Well, the nature of DEM data is that it can be a bit confusing and it takes some reading and experimentation to truly get the best data and the best results. Terrain Party has made a strong effort to remove much of that confusion, but you can still see the uncertainty is there because they provide multiple files with each download.
Currently there are two global data sets that represent the best quality we have world-wide (in the US there is higher quality data available for free, but worldwide it's lower resolution). Those data sets are SRTM, which used to be only 90 meters per pixel but a new version is now about 30m/pixel (1 arc second) which is called "SRTM 1", and then ASTER GDEM, which is also 30m/pixel. Generally SRTM is considered more accurate than ASTER, but sometimes you have to download and look at both to see as in some cases one data set looks better than the other for various reasons. Here's a discussion with some more info:https://www.researchgate.net/post/Which_DEM_data_is_better_for_elevation_mapping_ASTER_or_SRTM_satellite_data
Fortunately both are available from the USGS Earth Explorer site, so it's not really that hard to test both.
There is also another newer data set that looks promising called ALOS which may be worth looking at: http://www.eorc.jaxa.jp/ALOS/en/aw3d30/
I tested your area of interest and found some possible detail advantages, however there were some severe spikes of bad data right on the lake edge, so unless you have the means to merge data easily, or clean it up in some other way, the minor additional detail probably isn't worth it. I am hopeful this data set will be improved over time and may ultimately be better than ASTER and SRTM1 in the long run.
Anyway as far as I can see Terrain Party only offers the ASTER data in 30m/pixel, so that's a disadvantage, however I will say that this is better than what they used to offer, so it's clear they're working to improve on a consistent basis which is great. I'm not a big fan of PNG as a DEM data format for various reasons, but I'll admit it's more accessible and widely supported, so I understand the decision to use it. Now that they offer ASTER and a merged product based on other sources (except SRTM1) that can make up for some of the issues in ASTER, it's a decent source, and I'll have to apologize for not re-checking what they are currently offering before leveling criticism earlier. The last time I tested their data was probably 3-6 months ago and it was more limited and lower quality.
As far as the raw ASTER and SRTM1 data itself, it isn't going to look right in Photoshop. The only reason the Terrain Party stuff does is it uses 16 bit PNG, and PNG is a more widely supported format in image editors. There are good reasons to not use the PNG format however, including greater accuracy and important meta data like georeferencing info (which World Machine doesn't read at present, but is useful in other applications like Terragen).
So in the end Terrain Party is overall a decent option. It's great for *ease of use*, it is absolutely the easiest approach to get the data you want. It does not guarantee highest quality, so if quality is a concern, go with the USGS ASTER or SRTM source, but currently the difference is not huge.
If you want to directly access either SRTM1 or ASTER data you can find both here: https://earthexplorer.usgs.gov/
You'll need an account to download it, but it's free. The ASTER data also has particular usage restrictions, but is still free to download.
Your area of interest appears to be near a tile boundary, but the tile I got was 3601x3601 in both ASTER and SRTM 1. It's hard to say but I think the SRTM 1 data is slightly more accurate/detailed. You'll need 2 tiles to get the whole lake since it's right at a tile boundary.