I have only learned a few chords in my harmony and voice leading book. I, I6, V, V6, ii, ii6, IV and the inversions of V7. I am now trying to harmonize this melody and so far the most idiomatic bassline to use for this descending line according to my book is a a pattern of 10ths between bass and soprano. So in this case it would be I6,V43,I with 5^4^3 in the soprano. However, in this case it wont work because the ^6 before the descending line is a subdominant harmony and would need to go to a dominant chord. My bassline for the ^5^4^3 doesnt really work I think. That said would my only other option be V, V7 ,I?
Idiomatically, the best options in this specific instance are:
- The given solution
- Parallel 10ths
- Voice exchange
I mention this first only to reiterate what's already written in the OP. Parallel 3rds, 6ths, and 10ths are highly idiomatic, so that's always a good place to start when considering a harmonization. See below for why it's a very good solution in this particular case.
Contrary motion / voice exchange
Another highly idiomatic option is to counter the soprano 5-4-3 with 3-4-5. This is called "voice exchange", because the soprano and bass (in this case) swap scale degrees 3 and 5. Harmonically this would generally be I6-IV-I64 or, less commonly, I6-ii6-iii.
Voice exchange is just a special case of contrary motion. Once could just as well accompany 5-4-3 with 1-2-3, and harmonizing with I-V43-I6.
Regarding IV proceeding to V
This is not the only option for IV. IV (and, less commonly, ii) can also be used to prolong a I chord. I-IV-I is a perfectly acceptable progression.
This means that parallel tenths will work very well for the harmonization of the melody given in the OP.