Singing slowly is helpful for meditation and thinking on the words one is singing while combining it with the proper heart attitude. OTOH, I guess it might be more difficult to learn a new tune that way since one cannot see the big picture of the tune as well.
Perhaps I am not the best to answer this question, since I actually like most of the tunes recommended by the
Scottish Psalmody (and I have musical training), and I do not believe tunes are that important and so prefer simpler and plain tunes for worship (but then again, that was not the question you asked...you only asked concerning simplicity and tempo). The tunes recommended are generally plain but have a lot of heart. This webpage has a few recommendations.
http://psalmsingers.com/wp-content/...ew-Psalmsingers-For-Supplement-on-website.pdf
Here are some tunes on the simpler end of the spectrum for various psalm moods. I don't know how many are in the app or how fast they are sung in the app, so you can check for them. They are all C.M. unless otherwise noted. I omitted a number of ones I like because I otherwise would be listing almost all of the recommended tunes (and I typed this post quickly)!
Seem to work well with a wide variety of Psalms
Evan
Kilmarnock
Stracathro
Happy/Restful
Consolation
Denfield
Farrant
Huddersfield
Irish
Jackson
Rest
Praetorius
Sheffield
St. Asaph
St. Lawrence
St. Magnus
Tiverton
Weymouth
Thoughtful (can work with sad/plaintive psalms reasonably well too)
Ayrshire
Cunningham
Martyrdom
Naomi
Palestrina
St. Andrew
St. Flavian
St. Matthew
St. Paul
Sad/Plaintive
Bangor
Cheshire
Culross
Dundee (Windsor)
Martyrs
Orphan's
Soldau (L.M., often used with Psalm 6 first version)
St. Kilda
St. Mary
St. Neot
Walsall
Royal/Trusting (can work with jubilant psalms reasonably well too)
Arnold
French
Malan (S.M., sometimes used with Psalm 45 first version)
Narenza (S.M., sometimes used with Psalm 45 first version)
Petersham
St. Agnes
St. Anne
St. Columba
St. David
St. Leonard
Some tunes I have heard used with some psalms
St. Peter is often used with Psalm 1.
Westminster with Psalm 2.
Soldau Psalm 6 first version.
St. Matthias for Psalm 20.
Bangor or St. Mary for the first half of Psalm 22. Works for the second half too, but could choose a less sad tune (I am partial to Sheffield or Kilmarnock).
Crimond with Psalm 23.
St. Magnus with Psalm 24.
St. Matthew with Psalm 34.
Arnold, Malan (S.M.), Narezna (S.M.), Golden Hill (S.M.) Psalm 45.
Stroudwater Psalm 46.
St. Kilda or Orphan's with Psalm 51.
Rest or Jackson with Psalm 63.
Selma (S.M.), Zurich (S.M.), or Garelochside (S.M.) with Psalm 67.
Effingham often used with last three verses of Psalm 72.
Wetherby for last part of Psalm 73.
Morven Psalm 80.
Old 100th (L.M.), Caithness with Psalm 100
Consolation or Southwark with Psalm 110
Cunningham Psalm 116.
Tiverton or Praetorius Psalm 117.
Coleshill Psalm 118, especially the last half
French with Psalm 121.
Martyrdom with Psalm 130.
Newington Psalm 133.
Babel's Streams or Dunlapscreek with Psalm 137.
Paisley Psalm 143.
Other Tunes
Forest Green is a nice perky, simple tune that children seem to love. It works well for jubilant psalms like 98 and 150.
Somewhat more difficult, but I do like Milton as a tune for jubilant Psalms.
People have complained about Ericstane being difficult, but I find it useful as another thoughtful or sad/plaintive tune.
I like Glencairn with Psalm 42, but I don't think it is in the app, and I have not heard it frequently used.
A friend and I like Land of Rest, especially with Psalm 8; and Bays of Harris for various psalms (e.g., 23, 107), but these might be more difficult to find (and I'm not sure if they're in the app).
For learning tunes, I found it helpful (coming from a background of uninspired hymns and CCM only) to listen to the psalms while driving to work. It may be useful to have some playing throughout the day, especially maybe one that is sung to a tune you are working on. For more places where you can find tunes, see
here.
I also would not recommend learning a lot of tunes at once. Stick with one or with a small handful (to cover the spectrum of moods well enough). Maybe learn two from the sad/plaintive category (Dundee, St. Kilda, or Martyrs are fairly simple), one from the category that works well with most psalms (Evan or Kilmarnock might be simplest), and then use familiar hymn tunes for other psalms for now (e.g., New Britain and Denfield). And then expand here and there once you have those down.
Learning new tunes can be a lot of work, but it can be done and is rewarding in the end! I went from knowing none of them to knowing a lot of them.
Edit: Tallis and Moravia may also be simpler tunes since they have a bar that's the same or basically the same, so you only have to learn 3 bars with them instead of 4. Ballerma almost has the same bar twice too. Grafenberg is also simple. Ok, I'll stop now.