Select committees are supposed to scrutinise the work of the government, so there's one per department plus some others. As well as the opposition shadow ministers scrutinising ministers on the floor of the House of Commons (and Lords), they are supposed to be a calmer, more cross-party environment for backbenchers to scrutinise in more detail rather than performing for the cameras. As select committee meetings are also broadcast, often on rolling news when there is something a bit juicy, it's not clear whether they're always fulfilling that purpose.
APPGs are more for any group of MPs to get together and talk about an issue they're interested in. These can be very active or very inactive, big or small. They don't really have an official role in the parliamentary process. Some can be essentially a front for companies that want to lobby parliament/government.
With the Lords, yes, membership is growing as PMs have near-unlimited ability to appoint more members. I think the minimum level of reform that is going to need to happen at some point is to reduce that number. That said, it's worth saying that many members don't attend that often – and it's designed so that members can just pop along when something that matches their interests/specialisms comes up, rather than attending every day like a full-time MP, which is why Lords are paid a daily payment on days they attend rather than an annual salary.
(I've moved this over to the AUA thread as I thought it would fit quite well!)