The south of England is an easy place to camp badly: too far to drive on a Friday night, a field that looked empty online and is a slope in person, and a kit list copied from a week in Scotland. A first weekend should be closer, drier in intention, and short enough that you are glad you went.
Two nights, one field
Leave on Friday only if you can arrive in daylight. A Saturday arrival is often better. You pitch once, you have a full day on Sunday morning, and you are home before the week starts. The New Forest, the South Downs, and the quieter bits of the Sussex and Dorset coast all work if you pick a site with toilets and a tap. For a first night, a campsite with those two things is worth more than a wilder pitch you are not yet equipped for.
Kit that matters
A tent you have put up once in the garden, a sleeping bag rated for colder than the forecast, and a roll mat you have actually lain on. The ground in a southern English field in October is damp even when the day was fine. A cheap mat is the difference between sleeping and enduring. Take a stove you know how to light, one proper meal, and breakfast that does not need a talent for cooking in the wind. Spare pegs. A torch that is not your phone.
The day
Walk from the site rather than driving a second attraction into the weekend. The Downs, a forest track, or a stretch of coast you can reach on foot is enough. Be back before you need the torch to find the guy lines. If rain is forecast for the night, pitch on the higher part of the pitch, doors away from the wind, and eat early. There is no prize for cooking in a storm to prove the stove works.
Going home
Take the tent down dry if you can, and if you cannot, hang it up the same day you get home. A wet tent left in the bag until next spring is how people decide they do not like camping. You liked the weekend. The mildew was a storage problem.
Keep the first trip close, short, and slightly over-equipped for the cold. The south has plenty of weekends like that.