If the grass is too long then yes strim first especially if its very wet - try and let it dry. TBH there is not point in throwing lots of money at a mower, I bought one for £80 from Tesco had it for 3 years when I went it get it serviced it needed some repairs and it was going to cost £82 so I just bought another for £90!
If your lawn is relatively small and you find trailing cables, oil and fuel problematic, another option might be a cordless cylinder lawn mower with a rechargeable battery.
Its claimed to be able to cut an area of 418m'2 (4500ft'2) on a single charge.
It weighs just over 30lb and comes with a collapsable grass collection box.
Several different makes available but the one that I saw was from coopers of stortford, for around £120.00, it may be worth considering.