Actually in the park you should be fine, the blue and red trails have winding climbs and they aren’t major ones
Watch out as its very loose out there at the moment, never seen it that loose before in the last 20 odd years
If your heading out of the park then head over to the back entrance, through the Buriton car park and out towards Harting hill and Beacon hill, some lovely views of the sea and the I.O.W as well as some great inland views
Harting is a mellow climb, Beacon is a steep one but you can zig zag your way up to the gate near the top