Sad to hear your wife died and left you in a predicament mate. You have your kids to consider and rightfully so, makes you a responsible father who is guarded over letting them meet potential 'aunties' too frequently. But your kids aren't young kids and they'll probably want to see you meet someone and be happy as they can tell when you get down and lonely.
I played the field to a certain extent wanting to date, to hold a woman and have my confidence boosted after a painful divorce. I felt wanted, although I knew I couldn't just give my heart to anyone, they had to make do with lust and good times.
But life is largely what we make it providing we have the cards to play how we want to. If you want to empty your saggy nuts(to put it crudely; ) go fill your boots, it's out there and there's no harm in dating to have fun. But it seems to me you maybe want a more, a meaningful relationship. My advice if you choose to go on a dating site is to look yourself in the mirror, sit down and describe yourself truthfully, no bullshit. Who you are and who you are looking for. Try and write a bit of self depreciating humour in about yourself, women like to laugh. If you can cook then it's a bonus they like. List your interests, don't overly put selfish interests though where it looks like you're a mountaineer or bivvied up angler or a cross country metal detector etc. If you like travel weekends away trips to seaside, countryside, even say you like a bit of shopping if they ask lol.
Come across as confident , they don't want to be a shoulder to cry on when you tell them about how down you've been, how much you're missing your Mrs, how your kids are struggling to cope etc etc. All that comes in time when you are in a loving relationship when you can trust and confide in one another. Put a few recent pics up of yourself, not ones holding a 30lb carp, on a big motorbike or against your flashy car or big house in background. It will only interest chancing gold diggers.
There are decent women out there, and the decent ones familiar with dating sites can soon spot genuine guys.
But if you want some fun I say go for it. Much fun to be had, even with saggy knackers mate. A gentle teabagging before putting your arms on your head whilst swinging your hips as you straddle, like those 70 clackers.
Good luck clacker knackers; )