Variations of Secret Santa

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We're hosting a few people who'd otherwise be on their own for Christmas, so there'll be 2 families with teen kids plus one toddler, plus 3 or 4 singles, 12 or 13 in total. I want to avoid present angst especially for the singles feeling obligated to bring gifts but at the same time I know a couple will feel bad/ignore if I say no presents at all. So I'm thinking of some kind of Secret Santa, limit the budget, one present each person, it just seems more sensible.

1. everyone brings a generic gift that goes in the pot and lucky dip on the day but ranging from toddler to teens to single bachelors to a grandmother risks everyone getting something so generic no one's really pleased

2. I do lucky dip on names and give everyone a name to buy for. Possibly best and I can 'fix it' a bit so for example the guy with absolutely no idea about teens doesn't get one.

3. on a recent thread some families played a sort of game whereby you rolled dice depending on the number you passed a present on, opened one, lost a turn etc. Mean Santa they called it. Any clear instructions on this?

4. Any other option?

We did something in the office secret santa pool a few years ago.

1 buy a generic present up to the agreed value.
2 draw lots to see what order people pick a present
3 No 1 person opens a random present.
4 No 2 person has a choice to steel number 1 's present or open another and so on as does everyone who goes after. Any person who has their present stolen gets to open another from the pile.

Was great fun - the most popular gifts exchanged hands half a dozen times or more.

We did number 3. All generic presents go in the middle, wrapped. Roll the dice, roll a 6 and you can choose a gift but don't unwrap it. Next person to roll a 6 can choose one from the middle or steal one. When all the middle presents have been taken, everyone opens what they have.

We find it works best if each person brings 4 or 5 small items (£2 limit we did) then everyone usually gets at least a couple to open at the end. Something "obvious" like a toblerone or tube of smarties will probably be popular. Everyone usually ends up trading at the end to get what they want anyway!

I'd give a helpful instruction such as 'please buy a £20 gift for a 35 year old woman who likes football, chocolate, and Nirvana'.

or the trading system sounds fun too.

I'd do a combination of 2 and 3.
One (fixed) secret Santa, and 2 generic gifts brought by each person (kids need to bring presents)
Follow the Sinterklaas rules (<a class="break-all" href="https://www.google.com/url?sa=t&source=web&rct=j&url=csa-eur.nl/wp-content/uploads/2016/12/Rules-dice-game-1.pdf&ved=2ahUKEwiIo9-L0LP0AhU_if0HHYUxBycQFnoECDAQAQ&usg=AOvVaw2t5E4drlTPl_wnyUFOg903" rel="nofollow" target="_blank">here for example so everyone leaves with a couple of gifts. It will also fill in some time if you need an afternoons entertainment!

Thanks!
I like the idea of 2/3 small gifts in the pot and then a version of sinterklass. As a few of them don't really know the others it could help break the ice too (and stops me having to be the one helping the others find something appropriate!)