Hi Eve,
Renting a car would definitely improve the easyness the check most of those, if not even all. Some are not that far away from each other...if you're not relying on public transport. I assume you'll be flying to/from Lisbon...and that will also play a role on what (and when) to visit each...Óbidos mates Peniche, just as Evora drags in Evoramonte (or even Monsaraz as day-trip from, although visiting the Alqueva Dam surrounding reason would also be pleasant). Marvão (staying @ either Castelo de Vide or Portalegre) could come into role after visiting the highlights of Tomar (i'd do it while travelling from Peniche/Óbidos to Portalegre, a road trip varying between 220-250km depending on selected route). In the end it's really a matter of knowing how many (of those 10) you wish to spend in Lisbon Sintra (32 would improve a lot your time in Sintra...where several musts are apart -as for walking within- from each other).
As of a last comment for the moment (regardless of what's your final choice for transport) i'd just point that Evoramonte is perhaps too small (and of a doubtful charm given some years ago castle nasty/poor reconstructions) to trouble your non-self-driving route; on the other hand...and since you might really get to Tomar...when heading east (towards Marvão/Portalegre) you'll come close to Tejo/Tagus river...where quick (yet charming) must-sees would come from Constância Town...and also Almourol's Castle (right in the middle of the river). This would be typical landscape/architecture for central Portugal.
If i might be of further help, do feel free to ask for.
Best Travel Wishes from Lisbon Metro!