Just some thoughts from reading all the replies. You've mentioned your combined earnings are about 42k (30/12), sticking these into a mortgage calculator gives you a figure of around 200k.
Minimum deposit is 5%, and as you seem to already be aware, the bigger your deposit the lower the LTV and the lesser the monthly payments are.
On a 200k property with a 10k deposit (5%) would require a mortgage of 190k and give you monthly payments of around £800-880/mth (based on a 30 yr term)
On a 200k property with a 20k deposit (10%) would require a mortgage of 180k and give you monthly payments of around £720-760/mth (based on a 30 yr term)
On a 200k property with a 40k deposit (20%) would require a mortgage of 160k and give you monthly payments of around £580-600/mth (based on a 30 yr term)
The above gives you an example of monthly payments based on the different LTV rates.
Have you had a look around the areas you wish to buy to see what you can afford? This will at least give you an idea of how much of a deposit you need to save.
As for saving for the deposit, you mentioned a HTB ISA, but with 1k in it? is this actually the HTB ISA, or a HTB LISA? It sounds more like the latter? The HTB ISA which was available 2 and a bit years ago allowed you to open the account with a 1k deposit to gain a £250 bonus.
Anyway from what i've read, you mentioned your current deposit savings are practically zero. You mentioned you and your wife also have some debt - Credit card for you, and overdraft for your wife? (When does your wifes free overdraft end? iirc from graduate accounts you normally get a year or 2 before they start applying interest). Either way a mortgage advisor/broker would tell you to clear those debts, as they will eat away at the total a lender will give you - there's a section called monthly commitments and this will include anything like student loan repayments, and any credit commitments, and this can reduce things quite drastically.
I had the mishap last year of running into this, i purchased my missus engagement ring on credit (i had the money in my account to pay instantly, but wanted the credit card protection). Anyway shortly after we found a house we liked and went through the process of putting in a bid, went to get an AIP, and the total amount they'd lend us came out something ridiculous like 30k under what it was with 0 debt. (the ring wasn't 30k!
). Thankfully they hadn't yet taken payment of the ring, so i was able to change the payment and clear the debt from my account.
Without rambling on too much, based on the details you've given so far, unless you've got a family member gifting you a substantial deposit (10k+), then i suspect you'll be spending at least the next 12 months clearing your existing debts, and putting savings aside for a deposit. Personally i think you'd be better switching to a HTB LISA (1k bonus for every 4k saved), so have a read up on those and see if it makes more sense switching. Someone earlier mentioned about the Governments HTB schemes, i think this works by you providing some money as a deposit, and then the government also providing some money as a deposit (as a loan) - say 10k/10k each. The loan value increases/decreases depending on whether the value of the house increases/decreases. So if it increases 10% then you'd now owe 11k on the deposit loan. From memory these are typically 5 year loans as well, so you'd need to ensure you can not only pay your monthly payments, but also save up enough to pay off the governments loan at the end. There was a thread on here a couple of months back with someone in this sort of situation where he'd been paying back the monthly mortgage amount, but wasn't putting enough aside to pay back the loan at the end. I think these schemes can be a little irresponsible as it can open doors to houses (no pun intended) for people that wouldn't necessarily be able to afford it under normal circumstances.
Final point, i think someone's already linked you to the mortgage guide that Martin Lewis has published, that covers pretty much everything you need to know about mortgages.