I would look more into the car seat thing, the First Class is a good seat, but as someone said above, it can be quite upright for a newborn, and also, you wouldn't have the option to transfer a sleeping baby into the house, which can be a godsend in the first year, whether you have a routine or not. If you're not bothered about it attaching onto a pram, this is really cheap at the moment and the side impact protection looks great - that's your main concern with the cheaper end of the market in the first seats, really.
Your second concern with the First Class as a seat is that you might decide, by the time your baby gets to that age, that you don't want them forward facing too early. Rear facing is much safer, so you might choose to go for an extended rear facing seat, in which case, your forward facing seat will be redundant. However, being a Group 0+1 seat, the First Class does allow rear facing until a maximum of 13kg, and the back is much taller than most infant seats, so you will probably be able to use it RF until the baby does hit the weight limit - anywhere from 18 months to 2.5 years, at a guess. Another option is to go for a seat which will take your child from whenever they outgrow the baby carrier, until they need only a booster. I think this tends to work out more expensive, but the convenience of the baby carrier in the first year might outweigh this. You may also choose to go for something like the Kiddy Infinity Pro or Comfort Pro, which has an impact shield instead of the more common 5-point harness. There are benefits to this which include being safer than a forward facing seat with 5 point harness in an accident, avoiding the problem of children being able to wriggle their arms out (almost all children at least try this), and it's really easy to move from car to car as well. So I think it's worth looking into the other options at Group 1 before you tie yourself into using a bog standard seat.
The cot you've picked is much smaller than a standard sized one (60 x 120cm) - I'd be wary with this, as it will mean you'll probably spend more buying the bedding and mattress, and also your baby will probably grow out of it before they are 18 months old. Would you be happy for them to go into a full sized single then? If not, you'll be buying a larger cot or a toddler bed (often sold as cotbeds) anyway - so it makes sense to go with one from the start. I like ikea for cots, they are cheap, they look nice, and they are standard size now as well, so you can buy sheets to fit them from anywhere. Another nice feature is that, aside from the very cheapest model, they are very easily converted into a bedside cot if you so wished, which is fantastic for breastfeeding at night in the early days and co-sleeping safely, and then eases the transition into a cot whenever you want to make that.
Good luck! :)